Question

P is the mid-point of an arc APB of a circle. Prove that the tangent drawn at P will be parallel to the chord AB.

Answer 1

Join AP and BP.

Since TPS is a tangent and PA is the chord of the circle.

∠BPT = ∠PAB  ...(Angles in alternate segments)

But

∠PBA = ∠PAB  ...(∵ PA = PB) 

∴ ∠BPT = ∠PBA

But these are alternate angles

∴ TPS || AB