Mathematical and Physical Journal
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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

(5 pont)

Deadline expired on January 10, 2014.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás ITT.

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.


Statistics:

4 students sent a solution.
5 points:Ágoston Péter, Fehér Zsombor, Simon 047 Péter.
2 points:1 student.

Problems in Mathematics of KöMaL, December 2013