MathNet 2018-part-04 — 181 problems (EN–VI) Question 94

Let $\triangle ABC$ be an acute triangle, with $AB \neq AC$. Let $D$ be the midpoint of the line segment $BC$, and let $E$ and $F$ be the projections of $D$ onto the sides $AB$ and $AC$, respectively. If $M$ is the midpoint of the line segment $EF$, and $O$ is the circumcenter of triangle $ABC$, prove that the lines $DM$ and $AO$ are parallel.

Caucasus Mathematical Olympiad