Question

If angle between two radii of a circle is 130⁰ , the angle between the tangents at the ends of radii is
(a) 90⁰ (b) 50⁰ (c) 70⁰ (d) 40⁰

Answer 1

Let PQ and RP be the radii of the circle with the centre O.
$\angle \mathrm{ROQ}=130°$
$\mathrm{RP}\perp \mathrm{OR}\mathrm{and}\mathrm{PQ}\perp \mathrm{OQ}$ (Radii are perpendicular to the tangent)
In quadrilateral ROQP,
$$\begin{gathered} \angle \mathrm{ORP}+\angle \mathrm{RPQ}+\angle \mathrm{PQO}+\angle \mathrm{QOR}=360° \\ \Rightarrow 90°+\angle \mathrm{RPQ}+90°+130°=360° \\ \Rightarrow \angle \mathrm{RPQ}=50° \end{gathered}$$
Hence, the correct answer is option (b).