Question

In the given figure, if O is the centre of a circle, $PQ$ is a chord and the tangent $PR$ at P makes an angle of ${50}^{\circ }$ with $PQ$, find $\angle POQ$.

• A. ${40}^{\circ }$
• B. ${80}^{\circ }$
• C. ${100}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

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

Since OP is perpendicular to PR

$\angle OPR$=${90}^{\circ }$

$\angle OPQ+\angle QPR={90}^{\circ }$

$\angle OPQ+50°={90}^{\circ }$

$\angle OPQ=\angle OQP={40}^{\circ }$

Again,

$\angle POQ+\angle OPQ+\angle OQP={180}^{\circ }$

$\angle POQ+{40}^{\circ }+{40}^{\circ }={180}^{\circ }$

$\angle POQ={180}^{\circ }–{40}^{\circ }–{40}^{\circ }$

= $100°$

option C is the answer.