Question

In Fig. 1, 'O' is the centre of a circle and $\angle OBA={60}^{\circ }$. Then $\angle ACB$ equals

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${75}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

Consider $△AOB$.

$OA=OB\Rightarrow \angle OAB=\angle OBA={60}^o$

By angle sum property, we get, $\angle AOB={60}^o$

Angle in subtended at the center is twice the angle subtended anywhere on the arc, so

$\angle ACB=\frac{1}{2}\angle AOB={30}^o$

So option D is the right answer.