MathNet 2019-part-05 — 184 problems (EN–VI) Question 173

Let $BH$ be an altitude in an acute-angled triangle $ABC$. Let $M$ and $N$ be the midpoints of $AH$ and $CH$, respectively. Let $BB'$ be a diameter in the circumcircle of $\triangle BMN$. Prove that $AB' = CB'$.