HOMOTHETIC EQUILATERAL TRIANGLES

Let A'B'C', A"B"C" be two homothetic equilateral triangles.

Conjecture: The Euler lines of the triangles A'B"C", B'C"A", C'A"B" are concurrent, and also the Euler lines of the triangles A"B'C', B"C'A', C"A'B', if no one of the 6 triangles is degenerated.

A. P. Hatzipolakis, Hyacithos #21357