Question 121
Let $ABCDE$ be a regular pentagon and let $c$ be the circle with diameter $AB$. Diagonals $AC$ and $AD$ intersect the circle $c$ at points $F$ and $G$, respectively. Line $FG$ intersects the side $AE$ at point $H$. Let $K$ be the midpoint of the side $DE$. Prove that points $F, H, E$, and $K$ are concyclic.