Question

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

• A. ${45}^o$
• B. ${55}^o$
• C. ${25}^o$
• D. ${35}^o$

Answer 1

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

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

We know that the angle inscribed at the center of the circle by an arc is twice the angle subtended at the circumference by the same arc.

$\angle AOC$ is the angle at the center and $\angle ADC$ is the angle at the circumference.

$\therefore \angle ADC=\frac{1}{2}\angle AOC=\frac{1}{2}({60}^o+{30}^o)={45}^o$