Question 94
Let $E$ and $F$ be such interior points on side $AB$ of rectangle $ABCD$ that $|AE| = |EF|$. The perpendicular at $AB$ through the point $E$ intersects the diagonal $AC$ at the point $G$, and the distances $FD$ and $BG$ intersect at the point $H$. Prove that triangles $FBH$ and $GHD$ have equal areas.