Question

The measure of angle subtended by an arc at the centre of a circle is (double/ half) the measure of the angle subtended by the arc at any point on the circle.

Answer 1

The angle subtended by an arc at the centre of a circle is twice the angle subtended by the arc at any point on the circle.


Here, the angle subtended by the arc BC at the centre is $\angle BOC,$ and at any other point A on the arc BAC is $\angle BAC.$

Using the exterior angle of $△BAO$ and $△AOC$ at O, it can be proved that $\angle BOC=2\times \angle BAC.$