If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of $80°$ as shown in the given figure, then the measure of $\angle POA$ is:

[IM

Question

If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of $80°$ as shown in the given figure, then the measure of $\angle POA$ is:

[IMAGE_1]

Accepted Answer

Step 1: $\angle APB = 80°$. $\angle AOB = 180° - 80° = 100°$ (supplementary). $\angle POA = \frac{\angle AOB}{2} = \frac{100°}{2} = 50°$.

Question

Solution