Question

Prove that the angle subtend in a semi circle is always ${90}^o$

Answer 1

We know that diameter is a chord passing through center and thus angle subtended by it on center is ${180}^0$

And we know that by angle subtended by chord on center is double of angle subtended by it on major segment .(In this case major segment and minor segment not defined. )

So angle subtended by chord on any point of circle = $\frac{{180}^0}{2}={90}^0$

Thus it is proved that angle subtended in a semicircle is always ${90}^0$