Πέμπτη 3 Ιανουαρίου 2013

MORLEY TRIANGLES Conjecture

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.

(*)The Roussel triangle Here and with figure Here

Antreas P. Hatzipolakis
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LOCUS PROBLEM

Problem by Antreas Hatzipolakis Solution by Francisco Javier García Capitán ETC LISTING OF Q X(72803)

  • EUCLID 4404
  • ETC
    X(5459) Let ABC be a triangle, let A', B', C' be the midpoints of BC, CA, AB. Let L_a be the perpendicular through A' ...
  • HOMOTHETIC TRIANGLES and EULER LINES
    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 ...