Circle chapter top 100 questions

Important 2 Marks Questions for Class 10 Maths Board are as follows- Question 1- Find the value of k for which the roots of the quadratic equation 2x2+kx+8=0, will have equal value. Question 2- Determine the AP whose third term is 5 and seventh term is 9. Question 3- If any point is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay. Question 4- If the line segment joining the points A(2,1) and B (5,-8) is trisected at the points P and Q, find the coordinates of P. Question 5- If, from an external point P of a circle with centre O, two tangents PA and PB are drawn such that ∠BPA=120, then show that OP = 2PA. Question 6- Prove that the tangent drawn to a circle at the end points of a diameter are parallel to each other. Question 7- Find the value of p for which the numbers 2p-1, 3p+1, 11 are in A.P. Hence find the numbers. Question 8- Find the coordinates of the points of trisection of the line segment joining the points A (7,-2) and B (1,-5). Question 9- Find the coordinates of the point on x-axis, which is equidistant from the points (-2,5) and (2,-3). Question 10- A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA Question 11- Which term of the A.P. 8, 14, 20, 26, …….. Will be 72 more than its 41st term? Question 12- A line intersect the y-axis at the points P and Q respectively. If (2,-5) is the midpoint of PQ, then find the coordinates of P and Q. Question 13- Solve for x: 43–√x2+5x−23–√=0 Question 14- Prove that the perpendicular drawn from the point of contact to the tnagent, passes through the centre of the circle. Question 15- Show that in two concentric circle, is bisected at the point of contact. Question 16- Find the ratio in which the point (-3,k) divides the line segment joining the points (-5,-4) and (-2,3). Hence find the value of k. Question 17- If the nth term of an A.P. is given by tn= 3n + 4, find the common difference of the A.P. and the sum of its first five terms. Question 18-  In the figure below, the radius of incircle of ΔABC of area 84 cm2 is 4 cm and the lengths of the segment AP and BP into which side AB is divided by the point of contact are 6 cm and 8 cm. Find the lengths of the sides AC and BC.