WAEC 2023 · Paper 1 · Q17

Circle geometry

In the diagram, $O$ is the centre of the circle; $|NT| = |ST|$ and $\angle NTS = 36^\circ$ . $RN$ and $RS$ are tangents at $N$ and $S$ . Find the measure of the angle marked $t$ .

Worked solution (try it first)

$t$ is between the tangent $SR$ and the chord $SN$ .
The angle between a tangent and a chord equals the angle in the alternate segment, which is the angle at $T$ opposite $SN$ .
So $t = \angle NTS = 36^\circ$ , option A.

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