Let $ABC$ be any triangle and $D, E, F$ the midpoints of $BC, CA, AB$. The medians $AD, BE$ and $CF$ intersect at point $S$. At least two of the quadrilaterals $AF SE, BDSF, CESD$ are cyclic. Show that the triangle $ABC$ is equilateral.
Problem
Source: Switzerland - Swiss MO 2005 p1
Tags: geometry, Equilateral, Medians, Centroid, Concyclic, cyclic quadrilateral