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. 7 cm B. 12 cm

C. 15 cm D. 24.5 cm

In Fig. 10.54, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

If is isosceles with AB = AC and C (O, r) is the incircle of the touching BC at L, prove that L bisect BC.

In Fig. 10.60, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at A. Prove that PL + LM = PN + MN.

In Fig 10.57, a circle is inscribed in a quadrilateral ABCD in which . If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius r of the circle.

In fig. 10.55, O is the centre of the circle and BCD is tangent to it at C. Prove that .

In Fig. 10.61, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

In Fig. 10.58, there are two concentric circles with centre O of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Two tangent segments PA and PB are drawn to a circle with centre O such that . Prove that OP = 2 AP.

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that is equilateral.

In Fig. 10.53, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.