Question 137
Let $ABC$ be any triangle and let $D, E, F$ be the center of the sides of $BC, CA, AB$. The centroids $AD, BE$ and $CF$ intersect at the centroid $S$. At least two of the squares
$$
AFSE, \quad BDSF, \quad CESD
$$
be chord quadrilaterals. Show that triangle $ABC$ is equilateral.
$$
AFSE, \quad BDSF, \quad CESD
$$
be chord quadrilaterals. Show that triangle $ABC$ is equilateral.