Question

In 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. 60°
• B. 45°
• C. 30°
• D. 90°

Answer 1

The correct option is B

45°

$\angle$ADC = $\frac{1}{2}$ $\angle$AOC (The 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)

= $\frac{1}{2}$ ($\angle$AOB + $\angle$BOC)

= $\frac{1}{2}$ (${60}^{\circ }$ + ${30}^{\circ }$)

= $\frac{1}{2}$ (${90}^{\circ }$) = ${45}^{\circ }$