If $O$ is centre of a circle and Chord $P Q$ makes an angle $50^{\circ}$ with the tangent $P R$ at t

Question

If $O$ is centre of a circle and Chord $P Q$ makes an angle $50^{\circ}$ with the tangent $P R$ at the point of contact $P$, find the angle made by the chord at the centre.\

Professor PC Thomas Classes · Answer

(b): Given, $\angle Q P R=50^{\circ}$\ $\because \quad O P=O Q$\ (Radius)\ $	herefore \quad \angle O P Q=\angle O Q P$\ (Angle opposite to equal sides are equal)\ Now, $\angle O P Q+\angle Q P R=90^{\circ}$\ $[\because$ Tangent is the perpendicular to the radius through the point of contact]\ $\Rightarrow \angle O P Q+50^{\circ}=90^{\circ} \Rightarrow \angle O P Q=40^{\circ}$ and $\angle O Q P=40^{\circ}$\ Now, by angle sum property of triangle