Question 113
Let $ABCD$ be a rectangle and $BC = 2 \cdot AB$. Let $E$ be the midpoint of $BC$ and $P$ an arbitrary inner point of $AD$. Let $F$ and $G$ be the feet of perpendiculars drawn correspondingly from $A$ to $BP$ and from $D$ to $CP$. Prove that the points $E, F, P, G$ are concyclic.