Question 75
Let $A B C$ be an acute triangle with $A B \neq A C$. Let $D$ be the midpoint of the side $[B C]$, and $E$ and $F$ the projections of $D$ onto the sides $A B$ and $A C$, respectively. If $M$ is the midpoint of the segment $[E F]$ and $O$ is the center of the circle circumscribed about the triangle $A B C$, prove that the lines $D M$ and $A O$ are parallel.