WAEC 2022 · Paper 1 · Q35

Circle geometry

The diagram shows triangle $PQR$ inscribed in a circle. $PS$ is a tangent to the circle at $P$ , $\angle QPR = 58^\circ$ and $\angle RPS = 73^\circ$ . Find $\angle PRQ$ .

Worked solution (try it first)

The angle between a tangent and a chord equals the angle in the alternate segment.
So $\angle PQR = \angle RPS = 73^\circ$ .
The angles of triangle $PQR$ add up to $180^\circ$ : $\angle PRQ = 180^\circ - 58^\circ - 73^\circ$ .
So $\angle PRQ = 49^\circ$ , option A.

Report a problem with this question