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

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.

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

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.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.