MathNet 2018-part-04 — 181 problems (EN–VI) Question 180

Let $AD$, $BE$, $CF$ be the altitudes of the triangle $ABC$ and let $K$, $L$, $M$ be the orthocenters of triangles $AEF$, $BFD$, $CDE$, respectively. Denote by $G_1$ and $G_2$ the barycenters of triangles $DEF$, $KLM$, respectively. Prove that $HG_1 = G_1G_2$, where $H$ is the orthocenter of $ABC$.

Severius Moldoveanu