Question 57
Let $AD$, $BE$, and $CF$ denote the altitudes of triangle $\triangle ABC$. Points $E'$ and $F'$ are the reflections of $E$ and $F$ over $AD$, respectively. The lines $BF'$ and $CE'$ intersect at $X$, while the lines $BE'$ and $CF'$ intersect at the point $Y$. Prove that if $H$ is the orthocenter of $\triangle ABC$, then the lines $AX$, $YH$, and $BC$ are concurrent.