In the given figure, two circles intersect each other at the points A and B. If PQ and PR are tangents to these circles from a point P on AB produced, show that PQ = PR.

In the given figure, AB is a direct common tangent to two intersecting circles. Their common chord when produced intersects AB at P. Prove that P is the mid-point of AB.

In the given figure, PAT is tangent at A. If ∠TAB = 70° and ∠BAC = 45°, find ∠ABC.

In the given figure, PAT is tangent at A to the circle with centre O. If ∠ABC = 35°, find :

(i) ∠TAC

(ii) ∠PAB