Question

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

• A. ${55}^{\circ }$
• B. ${45}^{\circ }$
• C. $(\frac{60}{2}{)}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B

${45}^{\circ }$

It can be observed that $\angle AOC=\angle AOB+\angle BOC$
$={60}^{\circ }+{30}^{\circ }=90$

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

So, $\angle ADC=\frac{1}{2}\angle AOC=\frac{1}{2}\times {90}^{\circ }={45}^{\circ }$

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