RO-TST 1987 Problem 8

Let $ABCD$ be a square and $a$ be the length of his edges. The segments $AE$ and $CF$ are perpendicular on the square's plane in the same half-space and they have the length $AE=a$ , $CF=b$ where $a<b<a\sqrt 3$ . If $K$ denoted the set of the interior points of the square $ABCD$ determine $\min_{M\in K} \left( \max ( EM, FM ) \right)$ and $\max_{M\in K} \left( \min (EM,FM) \right)$ .

Octavian Stanasila