Question

prove that an angle in a semicircle is a right angle.​

please help

Answer 1

Given :

A circle with centre O.

PQ is the diameter of circle.

substending $\angle\:PAQ$ at point A on the circle.

To prove :

$\angle\:PAQ = 90\degree$

Proof :

POQ is a straight line passing throught the centre of the circle O .

$\therefore\:angle\:substended\:by\:arcPQ\:at\:O\:is\:180\degree\\ \angle\:POQ =2 \angle\:PAQ\\ \frac{\angle\:POQ}{2}=\angle\:PAQ...\\ \frac{180}{2}=\angle\:PAQ\\\angle\:PAQ = 90\degree$

Hence, Proved.