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The area of a smaller circle is equal to the area of a sector of a larger circle with central angle $120^{\circ}$. The radii of the smaller and larger circles are '$r$' and '$R$' respectively. Find $r : R$.
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Solution:(a) A.T.Q.
$\pi r^2 = \frac{120}{360} \pi R^2$ [1 mark]
$\frac{r^2}{R^2} = \frac{1}{3}$ [1/2 mark]
$r : R = 1 : \sqrt{3}$ [1/2 mark]
$\pi r^2 = \frac{120}{360} \pi R^2$ [1 mark]
$\frac{r^2}{R^2} = \frac{1}{3}$ [1/2 mark]
$r : R = 1 : \sqrt{3}$ [1/2 mark]