MathNet 2015-part-02 — 191 problems (EN–VI) Question 29

Let $ABC$ be a right triangle with the right angle at $C$. Let $A'$, $B'$ and $C'$ be the pedals of the perpendiculars from the centroid of the triangle $ABC$ onto the lines $BC$, $CA$ and $AB$ respectively.
Determine the ratio of the areas of the triangles $A'B'C'$ and $ABC$.