WAEC 2022 · Paper 1 · Q31

In the diagram, $MNR$ is a tangent to the circle centre $O$ at $N$ and $\angle NOS = 108^\circ$ . Find $\angle SNR$ .

Worked solution (try it first)

$ON = OS$ (radii), so triangle $NOS$ is isosceles: $\angle ONS = \frac{180^\circ - 108^\circ}{2}$
$= 36^\circ$ .
A tangent is perpendicular to the radius at the point of contact, so $\angle ONR = 90^\circ$ .
So $\angle SNR = 90^\circ - 36^\circ$
$= 54^\circ$ , option C.
(Check: the angle between a tangent and a chord is half the angle at the centre, $\frac12 \times 108^\circ = 54^\circ$ .)