The number of inches in the perimeter of an equilateral triangle equals twice the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?

1. If the side is $x$, the circumradius is $\frac{\sqrt3}3x$, and the area of the circle is $\frac{\pi}3x^2$.
2. Setting perimeter $=2\times$area: $3x=\frac{2\pi}3x^2$, so $x=\frac9{2\pi}$.
3. Radius $=\frac{\sqrt3}3x=\frac{\sqrt3}3\cdot\frac9{2\pi}=\boxed{\dfrac{3\sqrt3}{2\pi}}$.