See the discussion in Hyacinthos #21341
Conjecture:
Let A'B'C' be the internal Morley triangle of triangle ABC and A"B"C" the (homothetic) Roussel equilateral triangle(*). The Euler Lines of A'B"C", B'C"A", C'A"B" are concurrent.
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Theorem 1. Let ABC be an equilateral triangle and P a point. The Euler lines of the triangles PBC,PCA,PAB are concurent.Denote the point ... -
Let ABC be a triangle. Denote: (N1),(N2), (N3) = the NPCs of IBC, ICA, IAB, resp. (12), (13) = the reflections of (N1) in BI, CI, resp. ...
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