Question

In the given figure, APB is a tangent to a circle with center O, at point P. If $\angle QPB={50}^{\circ }$ , then the measure of $\angle POQ$ is :

• A. ${120}^{\circ }$
• B. ${100}^{\circ }$
• C. ${140}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ }$

Tangent is perpendicular to radius at the point of contact. That gives:

$\angle OPB=\angle OPQ+\angle QPB=\angle OPQ+{50}^o={90}^o$

$\Rightarrow \angle OPQ={40}^o$.

Triangle $OPQ$ is isosceles since $OP=OQ$. So $\angle OPQ=\angle OQP={40}^o$.

Thus, $\angle POQ=180-40-40={100}^o$

So option B is the correct answer.