In the figure, $O$ is the centre of the circle. Find $\angle BAC$.
"

Given:

$O$ is the centre of the circle.

To do:

We have to find $\angle BAC$.

Solution:

$\angle AOB = 80^o$

$\angle AOC =110^o$

This implies,

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

$= 80^o+ 110^o$

$= 190^o$

Reflex $\angle BOC = 360^o - 190^o$

$= 170^o$

arc $BEC$ subtends $\angle BOC$ at the centre and $\angle BAC$ at the remaining part of the circle.

Therefore,

$\angle BOC = 2\angle BAC$

$170^o = 2\angle BAC$

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

$= 85^o$

Hence $\angle BAC = 85^o$.

Tutorialspoint

Updated on: 10-Oct-2022

45 Views

Kickstart Your Career

Get certified by completing the course

Get Started