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.

From an external point P, tangents PA are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of .

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.

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

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