Straight line $\displaystyle l$ passes through the center of a square $\displaystyle ABCD$, whose area is $\displaystyle 1$. Let $\displaystyle a, b, c, d$ denote the shortest distances between line $\displaystyle l$ and points $\displaystyle A, B, C, D$ respectively. How to prove that $\displaystyle a^2 + b^2 + c^2 + d^2 = 1$?