Problem

Source: 2023 Singapore MO Round 2 Senior Q1

Tags: geometry



Let $ABCD$ be a square, $E$ be a point on the side $DC$, $F$ and $G$ be the feet of the altitudes from $B$ to $AE$ and from $A$ to $BE$, respectively. Suppose $DF$ and $CG$ intersect at $H$. Prove that $\angle AHB=90^\circ$.