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A circle is drawn in a sector of a larger circle of radius $\mathrm{r}$, as shown in the adjacent figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the small circle is -
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The correct answer is:
$\frac{\mathrm{r}}{3}$
Say the radius of smaller circle is $\mathrm{x}$ Here $\mathrm{OP}=\mathrm{x} \operatorname{cosec} 30^{\circ}$
while $\mathrm{OQ}=\mathrm{r}=\mathrm{x}+\mathrm{x} \operatorname{cosec} 30^{\circ}$
$\mathrm{x}=\frac{\mathrm{r}}{3}$
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