Question 153
Let $\triangle ABC$ be an acute triangle with orthocenter $H$. Points $E$ and $F$ are on segments $\overline{AC}$ and $\overline{AB}$, respectively, such that $\angle EHF = 90^\circ$. Let $X$ be the foot of the altitude from $H$ to $\overline{EF}$. Prove that $\angle BXC = 90^\circ$.