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.
Join AP and BP.
Since TPS is a tangent and PA is the chord of the circle.
`∠`BPT = `∠`PAB (angles in alternate segments)
`∠`PBA = `∠`PAB (∵ PA = PB )
∴ `∠` BPT =`∠`PBA
But these are alternate angles
∴ TPS ll AB