# For an equilateral triangle, the ratio of the in-radius and the ex-radius is:

For an equilateral triangle, the ratio of the in-radius and the ex-radius is:
[A]$1 : 3$
[B]$1 : \sqrt{3}$
[C]$1 : \sqrt{2}$
[D]$1 : 2$

$\mathbf{1 : 2}$
In-radius $= \frac{side}{2\sqrt{3}}$
Circum-radius $= \frac{side}{\sqrt{3}}$
∴ Required ratio $= \frac{side}{2\sqrt{3}} : \frac{side}{\sqrt{3}}$
$= \sqrt{3} : 2\sqrt{3} = 1 : 2$
Hence option [D] is the right answer.