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.

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