WAEC 2019 · Paper 1 · Q38

Circle geometry
Plane mensuration

In the diagram, $O$ is the centre of the circle of radius $18\text{ cm}$ . If $\angle ZXY = 70^\circ$ , calculate the length of arc $ZY$ . $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

$\angle ZXY$ is at the circumference on arc $ZY$ .
The angle at the centre is twice it: $\angle ZOY = 140^\circ$ .
Arc length is $\frac{\theta}{360^\circ} \times 2\pi r$ : arc $ZY = \frac{140}{360} \times 2 \times \frac{22}{7} \times 18$ .
That is 44 cm, option C.

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