In the given figure, a tangent has been drawn at a point $P$ on the circle centred at $O$.\ If $\an

Question

In the given figure, a tangent has been drawn at a point $P$ on the circle centred at $O$.\ If $\angle T P Q=110^{\circ}$ then $\angle P O Q$ is equal to\

Professor PC Thomas Classes · Answer

(c):We know that the radius of a circle is always perpendicular to the tangent at the point of contact.\ So, $\angle T P O=90^{\circ}$\ Now, $\angle T P O+\angle O P Q=110^{\circ} \Rightarrow \angle O P Q=110^{\circ}-90^{\circ}=20^{\circ}$\ Also, $\angle O P Q=\angle O Q P=20^{\circ}$\ [Angles opposite to equal sides are equal]