JAMB 2003 · UME · Q27

In the diagram, $PQR$ is a straight line and $PS$ is a tangent to the circle $QRS$ , with $PS = SR$ and $\angle SPR = 40^\circ$ . Find $\angle PSQ$ .

Worked solution (try it first)

$PS = SR$ , so triangle $PSR$ is isosceles and the angles opposite the equal sides are equal: $\angle SRP = \angle SPR = 40^\circ$ .
$PQR$ is a straight line, so $\angle SRQ = 40^\circ$ .
The angle between tangent $PS$ and chord $SQ$ equals the angle in the alternate segment: $\angle PSQ = \angle SRQ = 40^\circ$ , option C.