In the figure, $O$ is the centre of the circle. If $\angle APB = 50^o$, find $\angle AOB$ and $\angle OAB$.
"

Given:

$O$ is the centre of the circle. $\angle APB = 50^o$.

To do:

We have to find $\angle AOB$ and $\angle OAB$.

Solution:

Arc $AB$ subtends $\angle AOB$ at the centre and $\angle APB$ on the remaining part of the circle.

This implies,

$\angle AOB = 2\angle APB$

$= 2 \times 50^o$

$= 100^o$

Join $AB$.

$\triangle AOB$ is an isosceles triangle in which,

$OA = OB$

Therefore,

$\angle OAB = \angle OBA$

$\angle OAB + \angle OBA = 180^o - 100^o$

$= 80^o$

$2\angle OAB = 80^o$

$\angle OAB =\frac{80^o}{2}$

$= 40^o$.

Tutorialspoint

Updated on: 10-Oct-2022

55 Views

Kickstart Your Career

Get certified by completing the course

Get Started