Page 1 :
GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , CH-10-CIRCLES, PRACTICE EXERCISE-10.1, Q.1 A point P is 13 cm from the, centre of the circle. The length of, the tangent drawn from P to the, circle is 12 cm. Find the radius of, the circle., Ans. Radius of the circle is 5 cm., Q.2 In two concentric circles, a, chord of length 24 cm of larger, circle becomes a tangent to the, smaller circle whose radius is 5 cm., Find the radius of the larger circle., Ans. The radius of the smaller circle, is 13 cm., Q.3 The radii of two concentric, circles are13 cm and 8 cm. AB is a, diameter of the bigger circle. BD is a, tangent to the smaller circle, touching it at D. Find the length AD., Ans. AD = 19 cm, , Q.6 In Fig. 10.16, if AB = AC, prove, that BE = EC., OR, ABC is an isosceles triangle in which, AB = AC, circumscribed about a, circle, as shown in Fig. 10.16. Prove, that the base is bisected by the, point of contact., , Q.4 In two concentric circles, prove, that all chords of the outer circle, which touch the inner are of equal, length., Q.5 In Fig. 10.39, O is the centre of, the circle. PA and PB are tangent, segments., Show, that, the, quadrilateral AOBP is cyclic., , Q.7 In Fig. 10.18, XP and XQ are, tangents from X to the circle with, centre O. R is a point on the circle., Prove that, XA + AR = XB + BR., , GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 1

Page 2 :
GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , Q.10 Prove that the tangents at the, extremities of any chord make, equal angles with the chord., , Q.8 In Fig. 1020, the sides AB, BC, and CA of triangle ABC touch a, circle with centre O and radius r at, P, Q and R respectively., , Q.11 Find the length of the tangent, drawn from a point whose distance, from the centre of a circle is 25 cm., Given that the radius of the circle is, 7 cm., Ans. Length of tangent from P = 24, cm., Q.12 In Fig. 10.19, the incircle of ∆, ABC touches the sides BC, CA and, AB at D, E and F respectively. Show, that, AF + BD + CE = AE + BF + CD =, (Perimeter of ∆ ABC), , Prove that:, (i) AB + CQ = AC + BQ, (ii) Area (∆ABC) = (Perimeter of, ∆ABC) × r, Q.9 From an external point P, two, tangents PA and PB are drawn to, the circle with centre O. Prove that, OP is the perpendicular bisector of, AB., , Q.13 In Fig. 10.21, two circles touch, each other at the point C. Prove that, the common tangent to the circles, at C, bisects the common tangent at, P and Q., , GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 2

Page 3 :
GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10MATHEMATICS, , as shown in Fie. 1027. Find AD, BE, and CF., , Q.14 In given figure,, l and m are two, parallel tangents at A and B, The, tangent at C makes an inter, intercept DE, between l and m. Prove that ∠DFE, = 90°., , Ans. AD = x = 7 cm, BE = y = 5 cm, and CF = z = 3 cm., Q.17 In Fig. 10.53, ABC is a right, triangle right-angled, angled at B such that, BC = 6 cm and AB = 8 cm. Find the, radius of its incircle., , Q.15 The radius of the incir, incircle of a, triangle is 4 cm and the segments, into which one side is divided by, the point of contact are 6 cm and 8, cm. Determine the other two sides, of the triangle., Ans. BC = 15 cm and AB = 13 cm, , Ans. 2cm, , Q.16 A circle is inscribed in a A ABC, having sides 8 cm, 10 cm and 12 cm, , “Always, Always keep in mind you aare unique- just like every body else”, GALACTIC INSTITUTE : D-94/49, 94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART, PART-II, II NEW DELHI Mob.8826181724, , Page 3