The arc of a circle subtending a right angle at any point of the circle in its alternate segment is a semi-circle.

Explanation

To Prove: `∠PAQ=90^@`
Proof: `POQ` is a straight line passing through center `O`.
`∴` Angle subtended by arc `PQ` at `O=∠POQ=180^@`
The angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle.
`∴∠POQ=2∠PAQ`
`∠POQ/2=∠PAQ
`180/2=∠PAQ`
`∠PAQ=90^@`
Hence proved.