For an equilateral triangle, the ratio of the in-radius and the outer-radius is

Answer: Option A

Let the side of equilateral ΔABC be a & r = in-radius & R = outer radius

$$\begin{array}{rl}& r=\frac{a}{2\sqrt{3}},R=\frac{a}{\sqrt{3}}\\ & r:R=\frac{a}{2\sqrt{3}}:\frac{a}{\sqrt{3}}=1:2\end{array}$$