Question

In figure, if PA and PB are tangents to circle with centre O such that $\angle APB={80}^{\circ }$, then $\angle OAB$ is equal to:

• A. ${25}^{\circ }$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$

$\angle AOB={180}^{\circ }-{80}^{\circ }={100}^{\circ }$
$\angle OAB=\angle OBA=\frac{1}{2}({180}^{\circ }-{100}^{\circ })$
$={40}^{\circ }$