MathNet 2018-part-06 — 181 problems (EN–VI) Question 100

In an acute triangle $ABC$ there is an altitude $AH$ and median $AM$. On lines $AB$ and $AC$ there are points $X$ and $Y$ so that $AX = XC$ and $AY = YB$. Prove that the midpoint of segment $XY$ is equidistant from points $H$ and $M$.