NL-NWO 2002 Problem 1

The sides of a $10$ by $10$ square $ABCD$ are reflective on the inside. A beam of light enters the square via the vertex $A$ and heads to the point $P$ on $CD$ with $CP = 3$ and $PD = 7$ . In $P$ it naturally reflects on the $CD$ side. The light beam can only leave the square via one of the angular points $A, B, C$ or $D$ . What is the distance that the light beam travels within the square before it leaves the square again? By which vertex does that happen?