Question

Prove that the angle in a semicircle is a right angle.

Answer 1

Now POQ is a straight line passing through center O.

$\therefore$ Angle subtended by arc PQ at O is

$\angle POQ=180°$

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.

$\therefore \angle POQ=2\angle PAQ$

$\frac{\angle POQ}{2}=\angle PAQ$

$\frac{180}{2}=\angle PAQ$

$\angle PAQ=90$

Hence proved.