In Fig. 10.52, PQ is tangent at a point R of the circle with centre O. If , find .

If AB, AC, PQ are tangents in Fig. 10.51 and AB = 5 cm, find the perimeter of .

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

If PA and PB are tangents from an outside point P. such that PA = 10 cm and . Find the length of chord AB.

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 .