Question

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

• A. ${45}^o$
• B. ${60}^o$
• C. ${22.5}^o$
• D. ${30}^o$

Answer 1

The correct option is A ${45}^o$

$\angle AOC=\angle AOB+\angle BOC$ $={60}^{\circ }+{30}^{\circ }={90}^{\circ }$

Arc ABC subtends $\angle AOC$ at centre of a circle and $\angle ADC$ on point D

Therefore

$\angle AOC=2\angle ADC$ (Angle subtended by arc at the centre is double the angle subtended by it at any point on circumference. )

${90}^{\circ }$=$2\angle ADC$

$\angle ADC$=${45}^{\circ }$

Therefore option A will be the answer.