smc

First, find the diameter of the circle. Plug in the circumference for the formula $C=\pi d$ to solve for $d$. $$100=\pi d$$ $$d=\frac{100}{\pi }$$ Since all of an inscribed square's vertices touch the circle, and one of the angles of the circle is $90^{\circ }$, the square's diagonal is the diameter of the circle. From the Pythagorean theorem (or 45-45-90 triangles), the side length is $\frac{50\sqrt{2}}{\pi }$ inches, which is answer choice $\boxed{\frac{50\sqrt{2}}{\pi }}$ .