Question

In the figure $A,B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC={30}^o$ and $\angle AOB={60}^o$. If $D$ is a point on the circle other than the arc $ABC$, find $\angle ADC$.

Answer 1

Here,

$\angle AOC=\angle AOB+\angle BOC$

$\Rightarrow \angle AOC=60°+30°$

$\Rightarrow \angle AOC=90°$

We know that angle subtended by an arc at center is double the angle subtended by it any point on the remaining part of the circle.

$\Rightarrow$$\angle ADC=\frac{1}{2}\angle AOC=\frac{1}{2}\times {90}^o={45}^o$