Iranian Geometry Olympiad 2020 (Elementary) P2
Posted: Sat Dec 12, 2020 4:57 pm
A parallelogram $ABCD$ is given $(AB \ne BC)$. Points $E$ and $G$ are chosen on the line $CD$ such that $AC$ is the angle bisector of both angles $\angle EAD$ and $\angle BAG$. The line $BC$ intersects $AE$ and $AG$ at $F$ and $H$, respectively. Prove that the line $FG$ passes through the midpoint of $HE$.