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.
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.
Another relationship between Napoleon cubic K005 and Neuberg cubic K001 The world of Triangle Geometry is very intrincate. There are many...
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