Let $ABCDE$ be a convex pentagon with five equal sides and right angles at $C$ and $D$. Let $P$ denote the intersection point of the diagonals $AC$ and $BD$. Prove that the segments $PA$ and $PD$ have the same length. (Gottfried Perz)
Problem
Source: 47th Austrian Mathematical Olympiad Beginners' Competition Problem 4
Tags: Austria, geometry, pentagon