KöMaL 2013 A602

Let ABC be a non-equilateral triangle. Consider those equilateral triangles XYZ whose vertices $X$, $Y$ and $Z$ lie on the lines $BC$, $CA$ and $AB$, respectively. Show that the locus of centers of such triangles XYZ is a pair of parallel lines which are perpendicular to the Euler line of the triangle ABC .