Question

In the given figure, O is the centre of the circle and $\angle AOC={120}^{\circ }$. Find $\angle BDC$.

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

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

Since BOA is the diameter,
$\angle AOC+\angle BOC={180}^{\circ }$
${120}^{\circ }+\angle BOC={180}^{\circ }$
$\angle BOC={60}^{\circ }$
$\angle BDC=\frac{1}{2}\left(\angle BOC\right)$
$\angle BDC={30}^{\circ }$
(The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle’s circumference. )