Question 58
In an acute triangle $ABC$ with $AB \lt AC$, points $D$, $E$ and $F$ are the feet of the altitudes drawn from vertices $A$, $B$ and $C$, respectively. Let the orthocenter of $ABC$ be $H$ and the midpoint of the side $BC$ be $M$. Point $K$ on the prolongation of the line segment $EM$ beyond $M$ and point $L$ on the line segment $FM$ satisfy $MK = ML = MD$. Prove that points $K$, $L$ and $H$ lie on a line.