WAEC 2019 · Paper 1 · Q39

Circle geometry

In the diagram, $RT$ is a tangent to the circle at $R$ , $\angle PQR = 70^\circ$ , $\angle QRT = 52^\circ$ , $\angle QSR = y$ and $\angle PRQ = x$ . Find the value of $y$ .

Worked solution (try it first)

$\angle QRT$ is between the tangent $RT$ and the chord $RQ$ .
The angle between a tangent and a chord equals the angle in the alternate segment, which is at $S$ .
So $y = \angle QSR = 52^\circ$ , option C.

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