JAMB 1998 · UME · Q31

Construction & loci
Plane mensuration

The locus of all points at a distance 8 cm from a point $N$ passes through points $T$ and $S$ . If $S$ is equidistant from $T$ and $N$ , find the area of triangle $STN$ .

Worked solution (try it first)

The locus of points 8 cm from $N$ is a circle of radius 8 cm, so $NT = NS = 8$ cm.
$S$ is equidistant from $T$ and $N$ , so $ST = SN = 8$ cm.
All three sides are 8 cm: the triangle is equilateral.
Use area $= \frac12ab\sin C$ with the $60^\circ$ angle: $\frac12 \times 8 \times 8 \times \sin60^\circ = 32 \times \frac{\sqrt3}{2}$ .
So the area is $16\sqrt3\text{ cm}^2$ , option B.

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