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 $\angle ADC$. [2 Marks]

[2 Marks]

Answer 1

It can be observed that,

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

[1 Mark]

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

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

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

[1 Mark]