MathNet 2015-part-07 — 185 problems (EN–VI) Question 47

Let $ABC$ be a triangle with orthocenter $H$; suppose that $AB = 13$, $BC = 14$, $CA = 15$. Let $G_{A}$ be the centroid of triangle $HBC$, and define $G_{B}, G_{C}$ similarly. Determine the area of triangle $G_{A} G_{B} G_{C}$.