Question 113
A unit square $ABCD$ and a circle $\Gamma$ have the following property: if $P$ is a point in the plane not contained in the interior of $\Gamma$, then $\min (\angle APB, \angle BPC, \angle CPD, \angle DPA) \leq 60^{\circ}$. The minimum possible area of $\Gamma$ can be expressed as $\frac{a \pi}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100a + b$.