Question

A circle is drawn in a sector of a larger circle of radius, 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

• A. $\frac{r}{2}$
• B. $\frac{r}{3}$
• C. $\frac{2\sqrt{3}r}{5}$
• D. $\frac{r}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{r}{3}$

$\frac{R}{\alpha }=\frac{1}{2}$
$\Rightarrow \alpha =2R$
Now $\alpha +R=r$
$3R=r$
$R=r/3$