Let ABC be a triangle and Ka, Kb, Kc the Brocard axes of
the triangles GBC, GCA, GAB, resp.
Let A'B'C' be a triangle homothetic and sharing the same
centroid G with ABC.
The reflections La,Lb,Lc of Ka,Kb,Kc in the sidelines B'C', C'A',
A'B' of A'B'C' resp. are concurrent.
See: ANOPOLIS list, Message 137
The first who will send a solution (synthetic or not) to list HYACINTHOS will win the book: F.G.-M.: Exercices d' Algebre (1198 pages)