{"id":4940,"date":"2016-05-19T09:49:00","date_gmt":"2016-05-19T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/"},"modified":"2023-03-22T15:19:45","modified_gmt":"2023-03-22T09:49:45","slug":"ncert-solutions-class-10-maths-exercise-10-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 10.2"},"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-class-10-maths-exercise-10-2\/#NCERT_Solutions_for_Class_10_Maths_Circles\" >NCERT Solutions for Class 10 Maths\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-class-10-maths-exercise-10-2\/#1_From_a_point_Q_the_length_of_the_tangent_to_a_circle_is_24_cm_and_the_distance_of_Q_from_the_centre_is_25_cm_The_radius_of_the_circle_is\" >1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is:<\/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-class-10-maths-exercise-10-2\/#2_In_figure_if_TP_and_TQ_are_the_two_tangents_to_a_circle_with_centre_O_so_that_POQ_then_PTQ_is_equal_to\" >2. In figure, if TP and TQ are the two tangents to a circle with centre O so that POQ =  then PTQ is equal to:<\/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-class-10-maths-exercise-10-2\/#3_If_tangents_PA_and_PB_from_a_point_P_to_a_circle_with_centre_O_are_inclined_to_each_other_at_angle_of_then_POA_is_equal_to\" >3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of , then POA is equal to:<\/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-class-10-maths-exercise-10-2\/#4_Prove_that_the_tangents_drawn_at_the_ends_of_a_diameter_of_a_circle_are_parallel\" >4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.<\/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-class-10-maths-exercise-10-2\/#5_Prove_that_the_perpendicular_at_the_point_of_contact_to_the_tangent_to_a_circle_passes_through_the_centre\" >5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.<\/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-class-10-maths-exercise-10-2\/#6_The_length_of_a_tangent_from_a_point_A_at_distance_5_cm_from_the_centre_of_the_circle_is_4_cm_Find_the_radius_of_the_circle\" >6. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the 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-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/#7_Two_concentric_circles_are_of_radii_5_cm_and_3_cm_Find_the_length_of_the_chord_of_the_larger_circle_which_touches_the_smaller_circle\" >7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.<\/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-class-10-maths-exercise-10-2\/#9_In_figure_XY_and_XY_are_two_parallel_tangents_to_a_circle_with_centre_O_and_another_tangent_AB_with_point_of_contact_C_intersecting_XY_at_A_and_XY_at_B_Prove_that_AOB\" >9. In figure, XY and X\u2019Y\u2019 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X\u2019Y\u2019 at B. Prove that AOB =<\/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-class-10-maths-exercise-10-2\/#10_Prove_that_the_angel_between_the_two_tangents_drawn_from_an_external_point_to_a_circle_is_supplementary_to_the_angle_subtended_by_the_line-segment_joining_the_points_of_contact_at_the_centre\" >10. Prove that the angel between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.<\/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-class-10-maths-exercise-10-2\/#11_Prove_that_the_parallelogram_circumscribing_a_circle_is_a_rhombus\" >11. Prove that the parallelogram circumscribing a circle is a rhombus.<\/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-class-10-maths-exercise-10-2\/#12_A_triangle_ABC_is_drawn_to_circumscribe_a_circle_of_radius_4_cm_such_that_the_segments_BD_and_DC_into_which_BC_is_divided_by_the_point_of_contact_D_are_of_lengths_8_cm_and_6_cm_respectively_see_figure_Find_the_sides_AB_and_AC\" >12. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure). Find the sides AB and AC.<\/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-class-10-maths-exercise-10-2\/#13_Prove_that_opposite_sides_of_a_quadrilateral_circumscribing_a_circle_subtend_supplementary_angles_at_the_centre_of_the_circle\" >13. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.<\/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-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/#NCERT_Solutions_for_Class_10_Maths_Exercise_102\" >NCERT Solutions for Class 10 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 10.2 Class 10 Maths 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 10 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 Maths Circles<\/strong><strong>\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-circles\/1216\/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\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 10.2\" width=\"173\" height=\"214\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Circles\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Circles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>In Q 1 to 3, choose the correct option and give justification.<\/strong><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_From_a_point_Q_the_length_of_the_tangent_to_a_circle_is_24_cm_and_the_distance_of_Q_from_the_centre_is_25_cm_The_radius_of_the_circle_is\"><\/span><strong>1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) 7 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) 12 cm <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 15 cm <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 24.5 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (A)<\/strong> <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image001.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPQ = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius<\/p>\n<p style=\"text-align: justify;\">through the point of contact]\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 138px; width: 199px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image005.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>In right triangle OPQ,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">[By Pythagoras theorem]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 29px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image011.png\" \/>= 625 \u2013 576 = 49<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/>OP = 7 cm<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_In_figure_if_TP_and_TQ_are_the_two_tangents_to_a_circle_with_centre_O_so_that_POQ_then_PTQ_is_equal_to\"><\/span><strong>2. In figure, if TP and TQ are the two tangents to a circle with centre O so that <\/strong><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/><strong>POQ = <\/strong><img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image012.png\" \/><strong> then <\/strong><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/><strong>PTQ is equal to:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1\" style=\"height: 158px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image013.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image014.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image015.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image016.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image017.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (B)<\/strong> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POQ = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image018.png\" \/>, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPT = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OQT = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius through the point of contact]\n<p style=\"text-align: justify;\">In quadrilateral OPTQ,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POQ + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPT + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OQT + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>PTQ = <img decoding=\"async\" style=\"height: 21px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Angle sum property of quadrilateral]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image020.png\" \/> + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>PTQ = <img decoding=\"async\" style=\"height: 21px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image021.png\" \/> + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>PTQ = <img decoding=\"async\" style=\"height: 21px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>PTQ = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image022.png\" \/><\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_If_tangents_PA_and_PB_from_a_point_P_to_a_circle_with_centre_O_are_inclined_to_each_other_at_angle_of_then_POA_is_equal_to\"><\/span><strong>3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of <\/strong><img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image016.png\" \/><strong>, then <\/strong><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/><strong>POA is equal to:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image023.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image014.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image015.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image016.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (A) <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image001.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPQ = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius<\/p>\n<p style=\"text-align: justify;\">through the point of contact]\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 10\" style=\"height: 143px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image024.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image025.png\" \/>BPA<\/p>\n<p style=\"text-align: justify;\">[Centre lies on the bisector of the<\/p>\n<p style=\"text-align: justify;\">angle between the two tangents]\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OPA,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAP + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POA = <img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Angle sum property of a triangle]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image028.png\" \/> + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POA = <img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image029.png\" \/> + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POA = <img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>POA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image030.png\" \/><\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Prove_that_the_tangents_drawn_at_the_ends_of_a_diameter_of_a_circle_are_parallel\"><\/span><strong>4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: PQ is a diameter of a circle with centre O.<\/p>\n<p style=\"text-align: justify;\">The lines AB and CD are the tangents at P and Q respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 150px; width: 266px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image032.png\" \/> CD<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since AB is a tangent to the circle at P and OP is the radius through the point of contact.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius through the point of contact]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image001.png\" \/> CD is a tangent to the circle at Q and OQ is the radius through the point of contact.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OQD = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius through the point of contact]\n<p style=\"text-align: justify;\">From eq. (i) and (ii), <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OQD<\/p>\n<p style=\"text-align: justify;\">But these form a pair of equal alternate angles also,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image032.png\" \/> CD<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Prove_that_the_perpendicular_at_the_point_of_contact_to_the_tangent_to_a_circle_passes_through_the_centre\"><\/span><strong>5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact and the radius essentially passes through the centre of the circle, therefore the perpendicular at the point of contact to the tangent to a circle passes through the centre.<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_The_length_of_a_tangent_from_a_point_A_at_distance_5_cm_from_the_centre_of_the_circle_is_4_cm_Find_the_radius_of_the_circle\"><\/span><strong>6. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that the tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius through the point of contact.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 12\" style=\"height: 136px; width: 213px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image033.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/> OPA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">[By Pythagoras theorem]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 29px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 29px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image011.png\" \/>= 9<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> OP = 3 cm<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Two_concentric_circles_are_of_radii_5_cm_and_3_cm_Find_the_length_of_the_chord_of_the_larger_circle_which_touches_the_smaller_circle\"><\/span><strong>7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let O be the common centre of the two concentric circles.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 184px; width: 186px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let AB be a chord of the larger circle which touches the smaller circle at P.<\/p>\n<p style=\"text-align: justify;\">Join OP and OA.<\/p>\n<p style=\"text-align: justify;\">Then, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/> OPA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">[The tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to the radius through the point of contact<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> OA<sup>2<\/sup> = OP<sup>2<\/sup> + AP<sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\">[By Pythagoras theorem]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 29px; width: 118px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image040.png\" \/>= 16<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AP = 4 cm<\/p>\n<p style=\"text-align: justify;\">Since the perpendicular from the centre of a circle to a chord bisects the chord, therefore<\/p>\n<p style=\"text-align: justify;\">AP = BP = 4 cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB = AP + BP<\/p>\n<p style=\"text-align: justify;\">= AP + AP = 2AP<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 17px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image041.png\" \/>= 8 cm<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>8. A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>AB + CD = AD + BC<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 148px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that the tangents from an external point to a circle are equal.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>AP = AS \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">BP = BQ \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">CR = CQ \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">DR = DS\u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">On adding eq. (i), (ii), (iii) and (iv), we get<\/p>\n<p style=\"text-align: justify;\">(AP + BP) + (CR + DR)<\/p>\n<p style=\"text-align: justify;\">= (AS + BQ) + (CQ + DS)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB + CD = (AS + DS) + (BQ + CQ)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB + CD = AD + BC<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 10.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_In_figure_XY_and_XY_are_two_parallel_tangents_to_a_circle_with_centre_O_and_another_tangent_AB_with_point_of_contact_C_intersecting_XY_at_A_and_XY_at_B_Prove_that_AOB\"><\/span><strong>9. In figure, XY and X\u2019Y\u2019 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X\u2019Y\u2019 at B. Prove that <\/strong><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/><strong>AOB = <\/strong><img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image043.png\" \/><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 146px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image044.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: In figure, XY and X\u2019Y\u2019 are two parallel tangents to a circle with centre O and another<\/p>\n<p style=\"text-align: justify;\">tangent AB with point of contact C intersecting XY at A and X\u2019Y\u2019 at B.<\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join OC<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 152px; width: 238px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OCA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">[Tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to<\/p>\n<p style=\"text-align: justify;\">the radius through the point of contact]\n<p style=\"text-align: justify;\">In right angled triangles OPA and OCA,<\/p>\n<p style=\"text-align: justify;\">OA = OA [Common]\n<p style=\"text-align: justify;\">AP = AC [Tangents from an external<\/p>\n<p style=\"text-align: justify;\">point to a circle are equal]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OPA <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image046.png\" \/>OCA<\/p>\n<p style=\"text-align: justify;\">[RHS congruence criterion]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAP = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAC [By C.P.C.T.]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAC = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image025.png\" \/>PAB \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Similarly, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBQ = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBC = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image025.png\" \/>QBA \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image001.png\" \/>XY <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image032.png\" \/> X\u2019Y\u2019 and a transversal AB intersects them.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>PAB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>QBA = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Sum of the consecutive interior angles on the same side of the transversal is <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/>]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image025.png\" \/>PAB + <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image025.png\" \/>QBA<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image048.png\" \/>\u2026\u2026\u2026.(v)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAC + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBC = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">[From eq. (iii) &amp; (iv)]\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>AOB,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAC + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBC + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Angel sum property of a triangle]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/> + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/>[From eq. (v)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence proved.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 10.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Prove_that_the_angel_between_the_two_tangents_drawn_from_an_external_point_to_a_circle_is_supplementary_to_the_angle_subtended_by_the_line-segment_joining_the_points_of_contact_at_the_centre\"><\/span><strong>10. Prove that the angel between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OPA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OCA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image003.png\" \/>\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 40\" style=\"height: 138px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image049.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">[Tangent at any point of a circle is <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image004.png\" \/> to<\/p>\n<p style=\"text-align: justify;\">the radius through the point of contact]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image001.png\" \/> OAPB is quadrilateral.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>APB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OAP + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>OBP = <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Angle sum property of a quadrilateral]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>APB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB + <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image017.png\" \/> + <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image017.png\" \/>= <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">[From eq. (i) &amp; (ii)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>APB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>APB and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB are supplementary.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 10.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Prove_that_the_parallelogram_circumscribing_a_circle_is_a_rhombus\"><\/span><strong>11. Prove that the parallelogram circumscribing a circle is a rhombus.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: ABCD is a parallelogram circumscribing a circle.<\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: ABCD is a rhombus.<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since, the tangents from an external point to a circle are equal.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>AP = AS \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 21\" style=\"height: 155px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">BP = BQ \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">CR = CQ \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">DR = DS\u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">On adding eq. (i), (ii), (iii) and (iv), we get<\/p>\n<p style=\"text-align: justify;\">(AP + BP) + (CR + DR)<\/p>\n<p style=\"text-align: justify;\">= (AS + BQ) + (CQ + DS)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB + CD = (AS + DS) + (BQ + CQ)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB + CD = AD + BC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB + AB = AD + AD<\/p>\n<p style=\"text-align: justify;\">[Opposite sides of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image032.png\" \/>gm are equal]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> 2AB = 2AD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> AB = AD<\/p>\n<p style=\"text-align: justify;\">But AB = CD and AD = BC<\/p>\n<p style=\"text-align: justify;\">[Opposite sides of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image032.png\" \/>gm]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>AB = BC = CD = AD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> Parallelogram ABCD is a rhombus.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 10.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_A_triangle_ABC_is_drawn_to_circumscribe_a_circle_of_radius_4_cm_such_that_the_segments_BD_and_DC_into_which_BC_is_divided_by_the_point_of_contact_D_are_of_lengths_8_cm_and_6_cm_respectively_see_figure_Find_the_sides_AB_and_AC\"><\/span><strong>12. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure). Find the sides AB and AC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 180px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Join OE and OF. Also join OA, OB and OC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 24\" style=\"height: 210px; width: 229px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since BD = 8 cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>BE = 8 cm<\/p>\n<p style=\"text-align: justify;\">[Tangents from an external point to a circle are equal]\n<p style=\"text-align: justify;\">Since CD = 6 cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>CF = 6 cm<\/p>\n<p style=\"text-align: justify;\">[Tangents from an external point to a circle are equal]\n<p style=\"text-align: justify;\">Let AE = AF = <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since OD = OE = OF = 4 cm<\/p>\n<p style=\"text-align: justify;\">[Radii of a circle are equal]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> Semi-perimeter of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>ABC = <img decoding=\"async\" style=\"height: 44px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image055.png\" \/> = <img decoding=\"async\" style=\"height: 27px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image056.png\" \/> cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>ABC = <img decoding=\"async\" style=\"height: 31px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 37px; width: 335px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 31px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image059.png\" \/> cm<sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\">Now, Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>ABC = Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OBC + Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OCA + Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OAB<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 31px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image059.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 31px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image059.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 31px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image059.png\" \/> = <img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image062.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 31px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image059.png\" \/> = <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">Squaring both sides,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image064.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image067.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>AB = <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image068.png\" \/> = 7 + 8 = 15 cm<\/p>\n<p style=\"text-align: justify;\">And AC = <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image069.png\" \/> = 7 + 6 = 13 cm<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 10.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_Prove_that_opposite_sides_of_a_quadrilateral_circumscribing_a_circle_subtend_supplementary_angles_at_the_centre_of_the_circle\"><\/span><strong>13. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: ABCD is a quadrilateral circumscribing a circle whose centre is O.<\/p>\n<p style=\"text-align: justify;\">To prove: (i) <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>COD = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/>(ii) <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>BOC + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOD = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">Construction: Join OP, OQ, OR and OS.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 26\" style=\"height: 165px; width: 190px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image070.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Proof: Since tangents from an external point to a circle are equal.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/>AP = AS,<\/p>\n<p style=\"text-align: justify;\">BP = BQ \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">CQ = CR<\/p>\n<p style=\"text-align: justify;\">DR = DS<\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OBP and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OBQ,<\/p>\n<p style=\"text-align: justify;\">OP = OQ [Radii of the same circle]\n<p style=\"text-align: justify;\">OB = OB [Common]\n<p style=\"text-align: justify;\">BP = BQ [From eq. (i)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image026.png\" \/>OPB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image046.png\" \/>OBQ [By SSS congruence criterion]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image071.png\" \/>[By C.P.C.T.]\n<p style=\"text-align: justify;\">Similarly, <img decoding=\"async\" style=\"height: 21px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image072.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image073.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image074.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since, the sum of all the angles round a point is equal to <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image075.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 307px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 303px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 27px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image078.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 27px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image008.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>COD = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">Similarly, we can prove that<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>BOC + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image002.png\" \/>AOD = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch10\/Ex10.2\/image047.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_102\"><\/span>NCERT Solutions for Class 10 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 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_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 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<strong><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\">the best app for CBSE\u00a0<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 10.2 Class 10 Maths 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 &#8230; <a title=\"NCERT Solutions for Class 10 Maths Exercise 10.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-10-2\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 10.2\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":30016,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[1042,283,438,321,1485,216],"class_list":["post-4940","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-ncert-solutions","tag-cbse-class-10-mathematics","tag-cbse-study-material","tag-class-10","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 10 Maths Exercise 10.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 10.2 in PDF format for free download. 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