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Equilateral Triangles

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  • xpolakis@otenet.gr
    Soient A ,B ,C les symetriques d un point M par rapport aux cotes BC,CA,AB d un triangle equilateral ABC. Demontrer que les droites AA ,BB ,CC sont
    Message 1 of 1 , Feb 23, 2001
      Soient A',B',C' les symetriques d'un point M par rapport aux cotes
      BC,CA,AB d'un triangle equilateral ABC. Demontrer que les droites
      AA',BB',CC' sont concourantes.
      (P. Aubert - G. Papelier: Exercices de geometrie analytique... I, p. 31, #38)

      Now, by changing the notation, let ABC be the reference triangle,
      P a notable point on ABC plane (= O, H, I, etc), and T = A*B*C* a notable
      equilateral triangle of ABC (Morley, Napoleon etc).
      For every (P,T) corresponds a point (according to above).

      We can also formulate loci problems:

      Which is the locus of the point of concurrence as the point M, in the problem
      above, moves on a given line/circle?
      (Application in the reference triangle:
      Equilateral triangle : Napoleon Triangle; line : Euler Line /
      circle : incircle or circumcircle of ABC)


      Antreas
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