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

Solution (By Examveda Team)

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

$$\eqalign{ & r = \frac{a}{{2\sqrt 3 }},\,\,\,R = \frac{a}{{\sqrt 3 }} \cr & r:R = \frac{a}{{2\sqrt 3 }}:\frac{a}{{\sqrt 3 }} = 1:2 \cr} $$