SHARYGIN 2021 Problem 3

Altitudes $AA_1,CC_1$ of acute-angles $ABC$ meet at point $H$ ; $B_0$ is the midpoint of $AC$ . A line passing through $B$ and parallel to $AC$ meets $B_0A_1 , B_0C_1$ at points $A',C'$ respectively. Prove that $AA',CC'$ and $BH$ concur.