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 ∠ACB = 50°, find :

(i) ∠TAB

(ii) ∠ADB

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

(i) ∠TAC

(ii) ∠PAB

In the given figure, PAT is tangent at A and BD is a diameter of the circle. If ∠ABD = 28° and ∠BDC = 52°, find :

(i) ∠TAD

(ii) ∠BAD

(iii) ∠PAB

(iv) ∠CBD