{"id":5008,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-10-6\/"},"modified":"2018-06-18T17:01:26","modified_gmt":"2018-06-18T11:31:26","slug":"ncert-solutions-for-class-9-maths-exercise-10-6","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 10.6"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#NCERT_Solutions_for_Class_9_Mathematics_Circles\" >NCERT Solutions for Class 9 Mathematics\u00a0Circles<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#_Prove_that_the_line_of_centres_of_two_intersecting_circles_subtends_equal_angles_at_the_two_points_of_intersection\" >. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#2_Two_chords_AB_and_CD_of_lengths_5_cm_and_11_cm_respectively_of_a_circle_are_parallel_to_each_other_and_are_on_opposite_sides_of_its_centre_If_the_distance_between_AB_and_CD_is_6_cm_find_he_radius_of_the_circle\" >2. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find he radius of the circle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#Using_Pythagoras_theorem\" >[Using Pythagoras theorem]<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#3_The_lengths_of_two_parallel_chords_of_a_circle_are_6_cm_and_8_cm_If_the_smaller_chord_is_at_a_distance_of_4_cm_from_the_centre_what_is_the_distance_of_the_other_chord_form_the_centre\" >3. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord form the centre?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#OA2_AE2_OE2_Using_Pythagoras_theorem\" >OA2 = AE2 + OE2 [Using Pythagoras theorem]<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#4_Let_vertex_of_an_angle_ABC_be_located_outside_a_circle_and_let_the_sides_of_the_angle_intersect_chords_AD_and_CE_with_the_circle_Prove_that_ABC_is_equal_to_half_the_difference_of_the_angles_subtended_by_the_chords_AC_and_DE_at_the_centre\" >4. Let vertex of an angle ABC be located outside a circle and let the sides of the angle intersect chords AD and CE with the circle. Prove that ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#5_Prove_that_the_circle_drawn_with_any_drawn_with_any_side_of_a_rhombus_as_a_diameter_passes_through_the_point_of_intersection_of_its_diagonals\" >5. Prove that the circle drawn with any drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#6_ABCD_is_a_parallelogram_The_circle_through_A_B_and_C_intersect_CD_produced_it_necessary_at_E_Prove_that_AE_AD\" >6. ABCD is a parallelogram. The circle through A, B and C intersect CD (produced it necessary) at E. Prove that AE = AD.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#7_AC_and_BD_are_chords_of_a_circle_which_bisect_each_other_Prove_that\" >7. AC and BD are chords of a circle which bisect each other. Prove that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#AC_and_BD_are_the_diameters_as_only_diameters_can_bisects_each_other_as_the_chords_of_the_circle\" >AC and BD are the diameters as only diameters can bisects each other as the chords of the circle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#8_Bisectors_of_angles_A_B_and_C_of_a_triangle_ABC_intersect_its_circumcircle_at_D_E_and_F_respectively_Prove_that_angles_of_the_triangle_are_and_respectively\" >8. Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that angles of the triangle are and respectively.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#Since_the_angles_in_the_same_segment_of_a_circle_are_equal\" >Since the angles in the same segment of a circle are equal.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#9_Two_congruent_circles_intersect_each_other_at_points_A_and_B_Through_A_any_line_segment_PAQ_is_drawn_so_that_P_Q_lie_on_the_two_circles_Prove_that_BP_BQ\" >9. Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#Since_equal_arcs_of_two_equal_circles_subtend_equal_angles_at_any_point_on_the_remaining_part_of_the_circle_then_we_have\" >Since equal arcs of two equal circles subtend equal angles at any point on the remaining part of the circle, then we have,<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#10_In_any_triangle_ABC_if_the_angle_bisector_of_and_perpendicular_bisector_of_BC_intersect_prove_that_they_intersect_on_the_circum_circle_of_the_triangle_ABC\" >10. In any triangle ABC, if the angle bisector of and perpendicular bisector of BC intersect, prove that they intersect on the circum circle of the triangle ABC.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#NCERT_Solutions_for_Class_9_Maths_Exercise_106\" >NCERT Solutions for Class 9 Maths Exercise 10.6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 10.6 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0<\/strong><strong>Circles\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-circles\/1244\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 10.6\" width=\"165\" height=\"213\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Circles\"><\/span>NCERT Solutions for Class 9 Mathematics\u00a0Circles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6><span class=\"ez-toc-section\" id=\"_Prove_that_the_line_of_centres_of_two_intersecting_circles_subtends_equal_angles_at_the_two_points_of_intersection\"><\/span><strong>. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>Let two circles with respective centers A and B intersect each other at points C and D.<\/p>\n<p><img decoding=\"async\" id=\"Picture 149\" style=\"height: 150px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image001.jpg\" \/><\/p>\n<p>We have to prove <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ACB = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ADB<\/p>\n<p>Proof: In triangles ABC and ABD,<\/p>\n<p>AC = AD = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image003.png\" \/><\/p>\n<p>BC = BD = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image003.png\" \/><\/p>\n<p>AB = AB [Common]\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>ABC <img decoding=\"async\" style=\"height: 18px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image006.png\" \/>ABD<\/p>\n[SSS rule of congruency]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ACB = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ADB [By CPCT]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"2_Two_chords_AB_and_CD_of_lengths_5_cm_and_11_cm_respectively_of_a_circle_are_parallel_to_each_other_and_are_on_opposite_sides_of_its_centre_If_the_distance_between_AB_and_CD_is_6_cm_find_he_radius_of_the_circle\"><\/span><strong>2. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find he radius of the circle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>Let O be the centre of the circle. Join OA and OC.<\/p>\n<p>Since perpendicular from the centre of the circle to the chord bisects the chord.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>AE = EB = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>AB = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>x 5 = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image009.png\" \/>cm<\/p>\n<p>And CF = FD = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>CD = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>x 11 = <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image010.png\" \/>cm<\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" id=\"Picture 152\" style=\"height: 213px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image011.jpg\" \/><\/p>\n<p>Let OE = <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image012.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>OF = <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image013.png\" \/><\/p>\n<p>Let radius of the circle be <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image014.png\" \/><\/p>\n<p>In right angled triangle AEO,<\/p>\n<p>AO<sup>2<\/sup> = AE<sup>2<\/sup> + OE<sup>2<\/sup><\/p>\n[Using Pythagoras theorem]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image015.png\" \/>&#8230;.(i)<\/p>\n<p>Again In right angled triangle CFO,<\/p>\n<p>OC<sup>2<\/sup> = CF<sup>2<\/sup> + OF<sup>2<\/sup><\/p>\n<h6><span class=\"ez-toc-section\" id=\"Using_Pythagoras_theorem\"><\/span>[Using Pythagoras theorem]<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image016.png\" \/>&#8230;.(ii)<\/p>\n<p>Equating eq. (i) and (ii),<\/p>\n<p><img decoding=\"async\" style=\"height: 49px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image017.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image018.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image019.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image020.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image021.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image022.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image023.png\" \/><\/p>\n<p>Now from eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image024.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image025.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image026.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 45px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image027.png\" \/>cm<\/p>\n<p>Hence radius of the circle is <img decoding=\"async\" style=\"height: 45px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image028.png\" \/>cm.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"3_The_lengths_of_two_parallel_chords_of_a_circle_are_6_cm_and_8_cm_If_the_smaller_chord_is_at_a_distance_of_4_cm_from_the_centre_what_is_the_distance_of_the_other_chord_form_the_centre\"><\/span><strong>3. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord form the centre?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>Let AB = 6 cm and CD = 8 cm are the chords of circle with centre O. Join OA and OC.<\/p>\n<p><img decoding=\"async\" id=\"Picture 164\" style=\"height: 152px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image029.jpg\" \/><\/p>\n<p>Since perpendicular from the centre of the circle to the chord bisects the chord.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>AE = EB = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>AB = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>x 6 = 3 cm<\/p>\n<p>And CF = FD = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>CD = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>x 8 = 4 cm<\/p>\n<p>Perpendicular distance of chord AB from the centre O is OE.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>OE = 4 cm<\/p>\n<p>Now in right angled triangle AOE,<\/p>\n<h6><span class=\"ez-toc-section\" id=\"OA2_AE2_OE2_Using_Pythagoras_theorem\"><\/span>OA<sup>2<\/sup> = AE<sup>2<\/sup> + OE<sup>2 <\/sup>[Using Pythagoras theorem]<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 20px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image030.png\" \/>= 3<sup>2<\/sup> + 4<sup>2<\/sup><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 20px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image030.png\" \/>= 9 + 16 = 25<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image003.png\" \/>= 5 cm<\/p>\n<p>Perpendicular distance of chord CD from the center O is OF.<\/p>\n<p>Now in right angled triangle OFC,<\/p>\n<p>OC<sup>2<\/sup> = CF<sup>2<\/sup> + OF<sup>2<\/sup> [Using Pythagoras theorem]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 20px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image030.png\" \/>= 4<sup>2<\/sup> + OF<sup>2<\/sup><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image031.png\" \/>= 16 + OF<sup>2<\/sup><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>OF<sup>2<\/sup> = 16<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>OF = 3cm<\/p>\n<p>Hence distance of other chord from the centre is 3 cm.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"4_Let_vertex_of_an_angle_ABC_be_located_outside_a_circle_and_let_the_sides_of_the_angle_intersect_chords_AD_and_CE_with_the_circle_Prove_that_ABC_is_equal_to_half_the_difference_of_the_angles_subtended_by_the_chords_AC_and_DE_at_the_centre\"><\/span><strong>4. Let vertex of an angle ABC be located outside a circle and let the sides of the angle intersect chords AD and CE with the circle. Prove that <\/strong><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/><strong>ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>Vertex B of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ABC is located outside the circle with centre O.<\/p>\n<p>Side AB intersects chord CE at point E and side BC intersects chord AD at point D with the circle.<\/p>\n<p><img decoding=\"async\" id=\"Picture 167\" style=\"height: 121px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image032.jpg\" \/><\/p>\n<p>We have to prove that<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ABC = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>[<img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOC \u2013 <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>DOE]\n<p>Join OA, OC, OE and OD.<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AOC = 2<img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AEC<\/p>\n[Angle subtended by an arc at the centre of the circle is twice the angle subtended by the same arc at any point in the alternate segment of the circle]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image033.png\" \/>AOC = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AEC &#8230;(i)<\/p>\n<p>Similarly <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image033.png\" \/>DOE = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DCE &#8230;.(ii)<\/p>\n<p>Subtracting eq. (ii) from eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>[<img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOC \u2013 <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>DOE] = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AEC \u2013 <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DCE &#8230;.(iii)<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AEC = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ADC<\/p>\n[Angles in same segment in circle] &#8230;.(iv)<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DCE = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DAE<\/p>\n[Angles in same segment in circle] &#8230;.(v)<\/p>\n<p>Using eq. (iv) and (v) in eq. (iii),<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>[<img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOC \u2013 <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>DOE]\n<p>= <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DAE + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ABD \u2013 <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>DAE<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>[<img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOC \u2013 <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>DOE] = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ABD<\/p>\n<p>Or <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image008.png\" \/>[<img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOC \u2013 <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>DOE] = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>ABC<\/p>\n<p>Hence proved.<\/p>\n<hr \/>\n<h6><span class=\"ez-toc-section\" id=\"5_Prove_that_the_circle_drawn_with_any_drawn_with_any_side_of_a_rhombus_as_a_diameter_passes_through_the_point_of_intersection_of_its_diagonals\"><\/span><strong>5. Prove that the circle drawn with any drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>Let ABCD be a rhombus in which diagonals AC and BD intersect each other at point O.<\/p>\n<p>As we know that diagonals of a rhombus bisect and perpendicular to each other.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image034.png\" \/><\/p>\n<p>And if we draw a circle with side AB as diameter, it will definitely <strong>pass through point O<\/strong> (the point intersection of diagonals) because then <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image034.png\" \/>will be the angle in a semi-circle.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"6_ABCD_is_a_parallelogram_The_circle_through_A_B_and_C_intersect_CD_produced_it_necessary_at_E_Prove_that_AE_AD\"><\/span><strong>6. ABCD is a parallelogram. The circle through A, B and C intersect CD (produced it necessary) at E. Prove that AE = AD.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" id=\"Picture 170\" style=\"height: 134px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image035.jpg\" \/><\/p>\n<p><strong>Ans. <\/strong>In figure (a),<\/p>\n<p>ABCD is a parallelogram.<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 &#8230;.(i)<\/p>\n<p>ABCE is a cyclic quadrilateral.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/> &#8230;.(ii)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/>&#8230;.(iii)<\/p>\n[Linear pair]\n<p>From eq. (ii) and (iii), <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 &#8230;.(iv)<\/p>\n<p>Now, from eq. (i) and (iv),<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AE = AD [Sides opposite to equal angles are equal]\n<h6><img decoding=\"async\" id=\"Picture 173\" style=\"height: 147px; width: 348px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image037.jpg\" \/><\/h6>\n<p>(a) (b)<\/p>\n<p>In figure (b),<\/p>\n<p>ABCD is a parallelogram.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 and <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>4<\/p>\n<p>Also AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image038.png\" \/>CD and BC meets them.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/>&#8230;.(i)<\/p>\n<p>And AD<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image038.png\" \/>BC and EC meets them.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 &#8230;.(ii) [Corresponding angles]\n<p>Since ABCE is a cyclic quadrilateral.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/> &#8230;.(iii)<\/p>\n<p>From eq. (i) and (iii),<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6<\/p>\n<p>But from eq. (ii), <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6<\/p>\n<p>Now in triangle AED,<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AE = AD [Sides opposite to equal angles]\n<p>Hence in both the cases, AE = AD<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"7_AC_and_BD_are_chords_of_a_circle_which_bisect_each_other_Prove_that\"><\/span><strong>7. AC and BD are chords of a circle which bisect each other. Prove that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>(i) AC and BD are diameters.<\/strong><\/p>\n<p><strong>(ii) ABCD is a rectangle.<\/strong><\/p>\n<p><strong>Ans. Given<\/strong>: AC and BD of a circle bisect each other at O.<\/p>\n<p>Then OA = OC and OB = OD<\/p>\n<p><strong>To prove<\/strong>: (i) AC and BD are the diameters. In other words, O is the centre of the circle.<\/p>\n<p>(ii) ABCD is a rectangle.<\/p>\n<p><strong>Proof<\/strong>: (i) In triangles AOD and BOC,<\/p>\n<p><strong><img decoding=\"async\" id=\"Picture 176\" style=\"height: 126px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image039.jpg\" \/><\/strong><\/p>\n<p>AO = OC [given]\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>AOD = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>BOC [Vertically opp.]\n<p>OD = OB [given]\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOD<img decoding=\"async\" style=\"height: 18px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image006.png\" \/>COB [SAS congruency]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AD = CB [By CPCT]\n<p>Similarly <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>AOB<img decoding=\"async\" style=\"height: 18px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image006.png\" \/>COD<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AB = CD<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image040.png\" \/>[Arcs opposite to equal chords]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image041.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image042.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AC = BD [Chords opposites to equal arcs]\n<h6><span class=\"ez-toc-section\" id=\"AC_and_BD_are_the_diameters_as_only_diameters_can_bisects_each_other_as_the_chords_of_the_circle\"><\/span><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>AC and BD are the diameters as only diameters can bisects each other as the chords of the circle.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p>(ii) Ac is the diameter. [Proved in (i)]\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>B = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image034.png\" \/>&#8230;.(i) [Angle in semi-circle]\n<p>Similarly BD is the diameter.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>A = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image034.png\" \/>&#8230;(ii) [Angle in semi-circle]\n<p>Now diameters AC = BD<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image043.png\" \/>[Arcs opposite to equal chords]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image044.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image045.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/>AD = BC [Chords corresponding to the equal arcs] &#8230;.(iii)<\/p>\n<p>Similarly AB = DC &#8230;.(iv)<\/p>\n<p>From eq. (i), (ii), (iii) and (iv), we observe that each angle of the quadrilateral is <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image034.png\" \/>and opposite sides are equal.<\/p>\n<p>Hence ABCD is a rectangle.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"8_Bisectors_of_angles_A_B_and_C_of_a_triangle_ABC_intersect_its_circumcircle_at_D_E_and_F_respectively_Prove_that_angles_of_the_triangle_are_and_respectively\"><\/span><strong>8. Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that angles of the triangle are <\/strong><img decoding=\"async\" style=\"height: 45px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image046.png\" \/><strong>and <\/strong><img decoding=\"async\" style=\"height: 45px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image047.png\" \/><strong>respectively.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong>According to question, AD is bisector of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>A.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 = <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image048.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 179\" style=\"height: 173px; width: 158px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image049.jpg\" \/><\/p>\n<p>And BE is the bisector of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>B.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>4 = <img decoding=\"async\" style=\"height: 41px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image050.png\" \/><\/p>\n<p>Also CF is the bisector of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>C.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>6 = <img decoding=\"async\" style=\"height: 41px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image051.png\" \/><\/p>\n<h6><span class=\"ez-toc-section\" id=\"Since_the_angles_in_the_same_segment_of_a_circle_are_equal\"><\/span>Since the angles in the same segment of a circle are equal.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>9 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 [angles subtended by <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image052.png\" \/>] &#8230;.(i)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>8 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5 [angles subtended by <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image053.png\" \/>] &#8230;.(ii)<\/p>\n<p>Adding both equations,<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>9 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>8 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>3 + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>5<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 41px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image054.png\" \/><\/p>\n<p>Similarly <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>E = <img decoding=\"async\" style=\"height: 41px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image055.png\" \/><\/p>\n<p>And <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>F = <img decoding=\"async\" style=\"height: 41px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image056.png\" \/><\/p>\n<p>In triangle DEF,<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>E + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>F = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image057.png\" \/>(<img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>E + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>F )<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 45px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image058.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 45px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image059.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 41px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image060.png\" \/>[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image061.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>A + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>B + <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>C = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image036.png\" \/>]\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>D = <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image062.png\" \/><\/p>\n<p>Similarly, we can prove that<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>E = <img decoding=\"async\" style=\"height: 41px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image063.png\" \/> and <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>F = <img decoding=\"async\" style=\"height: 41px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image064.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"9_Two_congruent_circles_intersect_each_other_at_points_A_and_B_Through_A_any_line_segment_PAQ_is_drawn_so_that_P_Q_lie_on_the_two_circles_Prove_that_BP_BQ\"><\/span><strong>9. Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. Given<\/strong>: Two equal circles intersect in A and B.<\/p>\n<p>A straight line through A meets the circles in P and Q.<\/p>\n<p><img decoding=\"async\" id=\"Picture 182\" style=\"height: 97px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image065.jpg\" \/><\/p>\n<p><strong>To prove<\/strong>: BP = BQ<\/p>\n<p><strong>Construction<\/strong>: Join A and B.<\/p>\n<p><strong>Proof:<\/strong> AB is a common chord and the circles are equal.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>Arc about the common chord are equal, i.e.,<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image066.png\" \/><\/p>\n<h6><span class=\"ez-toc-section\" id=\"Since_equal_arcs_of_two_equal_circles_subtend_equal_angles_at_any_point_on_the_remaining_part_of_the_circle_then_we_have\"><\/span>Since equal arcs of two equal circles subtend equal angles at any point on the remaining part of the circle, then we have,<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2<\/p>\n<p>In triangle PBQ,<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 [proved]\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>Sides opposite to equal angles of a triangle are equal.<\/p>\n<p>Then we have, BP = BQ<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 10.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"10_In_any_triangle_ABC_if_the_angle_bisector_of_and_perpendicular_bisector_of_BC_intersect_prove_that_they_intersect_on_the_circum_circle_of_the_triangle_ABC\"><\/span><strong>10. In any triangle ABC, if the angle bisector of <img decoding=\"async\" style=\"height: 18px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image067.png\" \/>and perpendicular bisector of BC intersect, prove that they intersect on the circum circle of the triangle ABC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Ans. <\/strong><strong>Given<\/strong>: ABC is a triangle and a circle passes through its vertices.<\/p>\n<p>Angle bisector of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>A and the perpendicular bisector (say <img decoding=\"async\" style=\"height: 19px; width: 9px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image068.png\" \/>) of its opposite side BC intersect each other at a point P.<\/p>\n<p><strong>To prove<\/strong>: Circumcircle of triangle ABC also passes through point P.<\/p>\n<p><strong>Proof<\/strong>: Since any point on the perpendicular bisector is equidistant from the end points of the corresponding side,<\/p>\n<p><img decoding=\"async\" id=\"Picture 185\" style=\"height: 167px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image069.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image004.png\" \/>BP = PC &#8230;.(i)<\/p>\n<p>Also we have <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>1 = <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>2 [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image061.png\" \/>AP is the bisector of <img decoding=\"async\" style=\"height: 17px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image002.png\" \/>A (given)] &#8230;.(ii)<\/p>\n<p>From eq. (i) and (ii) we observe that equal line segments are subtending equal angles in the same segment i.e., at point A of circumcircle of <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>ABC. Therefore BP and PC acts as chords of circumcircle of <img decoding=\"async\" style=\"height: 18px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image005.png\" \/>ABC and the corresponding congruent arcs <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image070.png\" \/>and <img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/10_6\/image071.png\" \/>acts as parts of circumcircle. Hence point P lies on the circumcircle. In other words, points A, B, P and C are concyclic (proved).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_106\"><\/span>NCERT Solutions for Class 9 Maths Exercise 10.6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 9 Maths Exercise 10.6 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter &#8230; <a title=\"NCERT Solutions for Class 9 Maths Exercise 10.6\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 10.6\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1376,281],"tags":[283,1344,321,1485,216],"class_list":["post-5008","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-09","category-ncert-solutions","tag-cbse-study-material","tag-class-9","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\" \/>\n<meta property=\"og:site_name\" content=\"myCBSEguide\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/mycbseguide\/\" \/>\n<meta property=\"article:published_time\" content=\"2016-05-19T06:19:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-06-18T11:31:26+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/09\/mycbseguide_n.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"599\" \/>\n\t<meta property=\"og:image:height\" content=\"242\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"myCBSEguide\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:site\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"myCBSEguide\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\"},\"author\":{\"name\":\"myCBSEguide\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65\"},\"headline\":\"NCERT Solutions for Class 9 Maths Exercise 10.6\",\"datePublished\":\"2016-05-19T06:19:00+00:00\",\"dateModified\":\"2018-06-18T11:31:26+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\"},\"wordCount\":1639,\"commentCount\":5,\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"keywords\":[\"CBSE Study Material\",\"Class 9\",\"Mathematics\",\"maths\",\"NCERT Solutions\"],\"articleSection\":[\"Mathematics\",\"NCERT Solutions\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\",\"name\":\"NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"datePublished\":\"2016-05-19T06:19:00+00:00\",\"dateModified\":\"2018-06-18T11:31:26+00:00\",\"description\":\"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\",\"breadcrumb\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage\",\"url\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"contentUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mycbseguide.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions\",\"item\":\"https:\/\/mycbseguide.com\/blog\/category\/ncert-solutions\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"NCERT Solutions for Class 9 Maths Exercise 10.6\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"name\":\"myCBSEguide\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\",\"name\":\"myCBSEguide\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"contentUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"width\":180,\"height\":180,\"caption\":\"myCBSEguide\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/mycbseguide\/\",\"https:\/\/x.com\/mycbseguide\",\"https:\/\/www.linkedin.com\/company\/mycbseguide\/\",\"http:\/\/in.pinterest.com\/mycbseguide\/\",\"https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65\",\"name\":\"myCBSEguide\",\"sameAs\":[\"http:\/\/mycbseguide.com\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide","description":"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide","og_description":"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","og_url":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/","og_site_name":"myCBSEguide","article_publisher":"https:\/\/www.facebook.com\/mycbseguide\/","article_published_time":"2016-05-19T06:19:00+00:00","article_modified_time":"2018-06-18T11:31:26+00:00","og_image":[{"width":599,"height":242,"url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/09\/mycbseguide_n.jpg","type":"image\/jpeg"}],"author":"myCBSEguide","twitter_card":"summary_large_image","twitter_creator":"@mycbseguide","twitter_site":"@mycbseguide","twitter_misc":{"Written by":"myCBSEguide","Est. reading time":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#article","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/"},"author":{"name":"myCBSEguide","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65"},"headline":"NCERT Solutions for Class 9 Maths Exercise 10.6","datePublished":"2016-05-19T06:19:00+00:00","dateModified":"2018-06-18T11:31:26+00:00","mainEntityOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/"},"wordCount":1639,"commentCount":5,"publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage"},"thumbnailUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","keywords":["CBSE Study Material","Class 9","Mathematics","maths","NCERT Solutions"],"articleSection":["Mathematics","NCERT Solutions"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/","url":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/","name":"NCERT Solutions for Class 9 Maths Exercise 10.6 | myCBSEguide","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage"},"thumbnailUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","datePublished":"2016-05-19T06:19:00+00:00","dateModified":"2018-06-18T11:31:26+00:00","description":"NCERT Solutions for Class 9 Maths Exercise 10.6 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","breadcrumb":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#primaryimage","url":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","contentUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-10-6\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mycbseguide.com\/blog\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions","item":"https:\/\/mycbseguide.com\/blog\/category\/ncert-solutions\/"},{"@type":"ListItem","position":3,"name":"NCERT Solutions for Class 9 Maths Exercise 10.6"}]},{"@type":"WebSite","@id":"https:\/\/mycbseguide.com\/blog\/#website","url":"https:\/\/mycbseguide.com\/blog\/","name":"myCBSEguide","description":"","publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mycbseguide.com\/blog\/#organization","name":"myCBSEguide","url":"https:\/\/mycbseguide.com\/blog\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","contentUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","width":180,"height":180,"caption":"myCBSEguide"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/mycbseguide\/","https:\/\/x.com\/mycbseguide","https:\/\/www.linkedin.com\/company\/mycbseguide\/","http:\/\/in.pinterest.com\/mycbseguide\/","https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ"]},{"@type":"Person","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65","name":"myCBSEguide","sameAs":["http:\/\/mycbseguide.com"]}]}},"_links":{"self":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/5008","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/comments?post=5008"}],"version-history":[{"count":4,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/5008\/revisions"}],"predecessor-version":[{"id":16953,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/5008\/revisions\/16953"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/"}],"wp:attachment":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/media?parent=5008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/categories?post=5008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/tags?post=5008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}