Iranian Geometry Olympiad 2020 (Elementary) P2

For discussing Olympiad level Geometry Problems
IftakharTausifFarhan
Posts:15
Joined:Sat Dec 12, 2020 3:33 pm
Iranian Geometry Olympiad 2020 (Elementary) P2

Unread post by IftakharTausifFarhan » 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 $HE$.

Post Reply