KöMaL 2018 B4989

The midpoints of sides $BC$, $CA$ and $AB$ of a triangle $ABC$ are $D$, $E$ and $F$, respectively. Let $S$ denote the centroid of the triangle. Assume that the perimeters of triangles $AFS$, $BDS$ are $CES$ equal. Show that triangle $ABC$ is equilateral.