Question 54
Quadrilateral $ABCD$ is circumscribed about a circle; diagonals $AC$ and $BD$ intersect at $E$. Rays $DA$ and $CB$ meet at $F$. Let $G$ be a point such that $ECGD$ is a parallelogram, and let $H$ be the reflection of $E$ across $AD$. Prove $D, H, F, G$ are concyclic.