Question

The angle subtended on a semicircle is a right angle.

Answer 1

To prove : $\angle APB={90}^0$

$\because$ We know angle subtended by an arc at centre is double the angle subtended at any point or circumference.

$\Rightarrow$ Angle subtended by arc $AB$ at $O=$ Double the angle subtended at $P$

$\Rightarrow \angle AOB=2\angle APB$

$\because AOB$ is a straight line.

$\Rightarrow \angle AOB={180}^0$

$\Rightarrow 2\angle APB={180}^0$

$\Rightarrow \angle APB={90}^0$

$\therefore$ Angle subtended by arc $AB$ or semi circle is ${90}^0$.