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 10 January 2014.
Sorry, the solution is available only in Hungarian. Google translation
A feladathoz kapcsolódó cikk: Blas Herrera Gómez: The notable configuration of inscribed equilateral triangles in a triangle. Elemente der Mathematik Volume 57 (2002), Issue 1, pp 26-31.