Question

In the figure, O is the centre of the circle.

Find $\angle BAC$.

Answer 1

In the circle with centre O

$\angle AOB={80}^{o}and\angle AOC={110}^o$

$\therefore \angle BOC=\angle AOB+\angle AOC$

$={80}^o+{110}^o={190}^o$

$\therefore Reflex\angle BOC={360}^o-{190}^o={170}^o$

Now are BEC subtends $\angle BOC$ at the centre and $\angle BAC$ at the remaining part of the

$\therefore \angle BOC=2\angle BAC$

$\Rightarrow {170}^o=2\angle BAC$

$\Rightarrow \angle BAC=\frac{{170}^o}{2}={85}^o$

$\therefore \angle BAC={85}^o$