Problem A. 602. (December 2013)
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 January 10, 2014.
Sorry, the solution is available only in Hungarian. Google translation
4 students sent a solution. 5 points: Ágoston Péter, Fehér Zsombor, Simon 047 Péter. 2 points: 1 student.