Question

In the given figure, PQ is a chord of a circle with centre O and PT is a tangent at P, such that ∠QPT = 60°. Then, ∠PRQ = ?


(a) 135°
(b) 150°
(c) 120°
(d) 110°

Answer 1

$$\begin{gathered} \left(\mathrm{c}\right)120° \\ \text{A}\mathrm{ngle}\mathrm{between}a\mathrm{chord}\mathrm{and}\text{a}\mathrm{tangent}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{angle}\mathrm{formed}\mathrm{in}\mathrm{the}\mathrm{corresponding}\mathrm{alternate}\mathrm{segment}. \\ \therefore \angle QPA=\angle PRQ \\ \angle QPA+\angle QPT={180}^0\left(\mathrm{linear}\mathrm{}\mathrm{pair}\right) \\ \mathrm{B}\mathrm{u}\mathrm{t}\mathrm{}\angle QPA=\left({180}^0-{60}^0\right)={120}^0 \\ \therefore \angle PRQ={120}^0 \end{gathered}$$