A. 602. 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.
Proposed by: András Hraskó, Budapest
Deadline expired on 10 January 2014.