Question 63
Let $ABC$ be an acute triangle with altitude $AD$. The bisectors of angles $BAD$, $CAD$, intersect side $BC$ at $E$, $F$, respectively. The circumcircle of triangle $AEF$ intersects sides $AB$, $AC$ at $G$, $H$, respectively. Prove that lines $EH$, $FG$, and $AD$ pass through a common point. (Patrik Bak)