MathNet 2018-part-04 — 181 problems (EN–VI) Question 106

In an acute triangle $ABC$ with $AB \lt BC$ let $BB'$ be an altitude, and let $O$ be the circumcenter. A line through $B'$ parallel to $CO$ meets $BO$ at $X$. Prove that $X$ and the midpoints of $AB$ and $AC$ are collinear.

Caucasus Mathematical Olympiad