Question

In the figure '$O$' is the centre of circle and $PQ$ is tangent of the circle. If $\angle RPQ={40}^o$, then find the measure of $\angle POR$.

Answer 1

We know that $OP\perp PQ(\because PQ\text{is tangent of the circle})$

$\Rightarrow \angle OPQ={90}^o\therefore \angle OPR={90}^o-\angle RPQ={90}^o-{40}^o={50}^o$

In isosceles $△OPR$, we know

$\angle OPR=\angle ORP$

Therefore, $\angle POR={180}^o-2\angle OPR=180-2\times 50={80}^o$