Question

Question 1
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 \(\angle ADC\).

Answer 1

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

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.

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

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