Problem #WSP-5304

Problem

Consider the point $H$ of intersection of the heights of the triangle $ABC$. Prove that Euler lines of the triangles $ABC$, $ABH$, $BCH$ and $ACH$ intersect at one point. On the diagram below the points $R,S,T$ are the points of intersection of medians in triangles $ABH$, $BCH$, and $ACH$ respectively.