MathNet 2024-part-04 — 168 problems (EN–VI) Question 160

Let $O$ and $I$ be the circumcenter, respectively the incenter of the triangle $ABC$. The incircle is tangent to the sides $BC$, $AC$ and $AB$ at the points $A'$, $B'$, respectively $C'$, and $G'$ is the centroid of the triangle $A'B'C'$. If $G'O = 7G'I$, prove that triangle $ABC$ is equilateral.

Marian Ursărescu