In the given figure, $O$ is the centre of the circle and $P Q$ is the chord. If the tangent $P R$ at

Question

In the given figure, $O$ is the centre of the circle and $P Q$ is the chord. If the tangent $P R$ at $P$ makes an angle of $50^{\circ}$ with $P Q$, then the measure of $\angle P O Q$ is\

Professor PC Thomas Classes · Answer

(c): $P R$ is tangent which touches circle at point $P$. So, $\angle O P R=90^{\circ}$ 
$$ \angle O P Q=90^{\circ}-\angle R P Q=90^{\circ}-50^{\circ}=40^{\circ} $$ In, $	riangle P O Q$, $$ O P=O Q $$ (Radii of circle)\ So, $\angle O Q P=\angle O P Q=40^{\circ}$\ $	herefore \quad \angle P O Q=180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}$\