Question

In the adjoining figure, two circles with centres O, C intersect at points A, B. The centre C of the smaller circle lies on the circumference of the other circle. If $\angle AOB={80}^o$, find $\angle APB$.

Answer 1

In the bigger circle with the centre O, $\angle ACB$ is the half of the reflex $\angle AOB$

Reflex $\angle AOB={360}^o-{80}^o={280}^o$

$\angle ACB=\frac{1}{2}\times {280}^o={140}^o$

Similarly, in the smaller circle with centre C, $\angle APB$ is the half of the $\angle ACB$

$\therefore \angle APB=\frac{1}{2}\times \angle ACB=\frac{1}{2}\times {140}^o={70}^o$