WAEC 2020 · Paper 1 · Q43

Circle geometry

In the diagram, $O$ is the centre of the circle. $PQ$ and $RS$ are tangents to the circle at the ends of a diameter. Find the value of $(m + n)^\circ$ .

Worked solution (try it first)

Each of $m$ and $n$ is an angle between a tangent and a chord, so each equals the angle in the alternate segment: they are the two angles of the triangle at the ends of the diameter, taken crosswise.
The third angle of the triangle stands on the diameter, so it is $90^\circ$ (angle in a semicircle).
So the two angles at the ends of the diameter add up to $180^\circ - 90^\circ = 90^\circ$ , and $m + n = 90^\circ$ , option B.

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