Question

Prove that equal chords of a circle subtends equal angle at the centre of a circle.

Answer 1

In the figure, $PQ$ and $RS$ are equal chords and $O$ is the centre of the circle.

$\Rightarrow$ In $△POQ$ and $△ROS:$

$OP=OROQ=OS\left(\text{radius of the circle}\right)$

and $PQ=RS$ (As given above)

$\therefore △POQ\cong △ROS$

We can say, $\angle POQ=\angle ROS$

Hence proved that equal chords of a circle subtend equal angle at the centre of a circle.