Question 133
In a convex quadrilateral $ABCD$, its diagonals meet at $E$, and $H$, $G$ are the midpoints of the sides $AD$, $BC$, respectively. The circumcircles $c_1$ and $c_2$ of the triangles $AEB$ and $DEC$, respectively, meet at the point $F \neq E$. If the parallel from $E$ to the line $HG$ meets the circle $c_2$ at $S$, prove that $FS \parallel CD$.