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(C) For an equilateral triangle $ABC$ with side length $a$,let $R$ be the circumradius and $r$ be the inradius.In an equilateral triangle,the circumra

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remains constant

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(C) For an equilateral triangle $ABC$ with side length $a$,let $R$ be the circumradius and $r$ be the inradius.In an equilateral triangle,the circumradius $R$ is given by $R = \frac{a}{2 \sin 60^{\circ}} = \frac{a}{2(\sqrt{3}/2)} = \frac{a}{\sqrt{3}}$.The inradius $r$ is given by $r = \frac{a}{2 	an 60^{\circ}} = \frac{a}{2\sqrt{3}}$.Therefore,the ratio $\frac{R}{r} = \frac{a/\sqrt{3}}{a/(2\sqrt{3})} = \frac{a}{\sqrt{3}} 	imes \frac{2\sqrt{3}}{a} = 2$.Since the ratio is $2$,which is independent of $a$,it remains constant.

Let $ABC$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $ABC$ respectively. Then,as a function of $a$,the ratio $\frac{R}{r}$

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