imc

Let $s$ be the length of a side of the equilateral triangle and let $r$ be the radius of the circle. In a circle with a radius $r$, the side of an inscribed equilateral triangle is $r\sqrt{3}$. So $s=r\sqrt{3}$. The perimeter of the triangle is $3s=3r\sqrt{3}$ The area of the circle is $\pi r^2$ So: $\pi r^2=3r\sqrt{3}$ $\pi r=3\sqrt{3}$ $r=\frac{3\sqrt{3}}{\pi }\Rightarrow \boxed{\frac{3\sqrt{3}}{\pi }}$