waecmaths question:
In a circle radius r cm, a chord is long 10cm from the centre of the circle. Find, correct to the nearest cm, the value of r
Option A:
22cm
Option B:
17cm
Option C:
16cm
Option D:
15cm
waecmaths solution:
$\begin{align} & AD=\tfrac{1}{2}AB\text{ }\!\!\{\!\!\text{ }OD\bot ar\text{ bisector of AB }\!\!\}\!\!\text{ } \\ & \text{Using pythagoras theorem} \\ & {{r}^{2}}={{(8\sqrt{3})}^{2}}+{{10}^{2}} \\ & {{r}^{2}}=192+100 \\ & r=\sqrt{292}=2\sqrt{73}=17.088 \\ & r\approx 17\text{ (to the nearest whole number)} \\\end{align}$
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