Question

In the figure, $O$ is the center of circle and $AB=AC$. Find $\angle BOC$.

• A. ${54}^o$
• B. ${56}^o$
• C. ${47}^o$
• D. ${27}^o$

Answer 1

The correct option is A ${54}^o$


We know, $AB=AC$
So,
$\angle AOB=\angle AOC\text{(Equal chords AB and AC make equal angles at center)}$
$\angle AOC={153}^o$

Now, $\angle AOB+\angle AOC+\angle BOC={360}^o$
${153}^o+{153}^o+\angle BOC={360}^o$
$\angle BOC={360}^o-{306}^o$
$\angle BOC={54}^o$

So, option $\left(a\right)$ correct.