Question 126
Three unit circles $\omega_{1}$, $\omega_{2}$, and $\omega_{3}$ in the plane have the property that each circle passes through the centers of the other two. A square $S$ surrounds the three circles in such a way that each of its four sides is tangent to at least one of $\omega_{1}$, $\omega_{2}$ and $\omega_{3}$. Find the side length of the square $S$.