In Figure, if tangents $P A$ and $P B$ from an external point $P$ to a circle with centre $O$, are i

Question

In Figure, if tangents $P A$ and $P B$ from an external point $P$ to a circle with centre $O$, are inclined to each other at an angle of $80^{\circ}$, then $\angle A O B$ is equal to\

Professor PC Thomas Classes · Answer

(a) : In quadrilateral $A O B P$ $$ \begin{aligned} & \angle A O B+\angle O B P+\angle A P B+\angle O A P=360^{\circ} \ \Rightarrow \quad & \angle A O B+90^{\circ}+90^{\circ}+80^{\circ}=360^{\circ} \ & {[\because O A \perp P A 	ext { and } O B \perp P B) } \ \Rightarrow \quad & \angle A O B=360^{\circ}-260^{\circ}=100^{\circ} \end{aligned} $$