Question 48
Pentagon $A B C D E$ is inscribed in a circle. Its diagonals $A C$ and $B D$ intersect at $F$. The bisectors of $\angle B A C$ and $\angle C D B$ intersect at $G$. Let $A G$ intersect $B D$ at $H$, let $D G$ intersect $A C$ at $I$, and let $E G$ intersect $A D$ at $J$. If $F H G I$ is cyclic and
$$
J A \cdot F C \cdot G H=J D \cdot F B \cdot G I
$$
prove that $G, F$ and $E$ are collinear.
$$
J A \cdot F C \cdot G H=J D \cdot F B \cdot G I
$$
prove that $G, F$ and $E$ are collinear.