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7419For the Russian members (was: Thebault point)

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  • Darij Grinberg
    Aug 3, 2003
      Dear all,

      In Hyacinthos message #7410, I wrote:

      >> >> > (1b) The Euler lines of triangles AB'C', BC'A',
      >> >> > CA'B' concur at one point on the
      >> >> > nine-point circle of triangle ABC.

      >> >> > and (1b) is a result of Victor Thebault.
      >> >> Notethat the common point is the center of
      >> >> Jerabek hyperbola.

      >> I have met this before. The point M where the Euler lines
      >> of triangles AB'C', BC'A', CA'B' meet has the property
      >> that one of the equations MA' = MB' + MC' or cyclically
      >> holds. This was stated by Thebault. Can anybody find a
      >> SYNTHETIC proof?

      I think that a synthetic proof (in Russian) can be found at

      http://archive.1september.ru/mat/2000/no43_1.htm

      Alas, I cannot follow the author's observation. Anybody who
      can help?

      Darij Grinberg

      PS: Thanks Jean-Pierre, perhaps your equations can be
      helpful in finding a synthetic proof.

      Darij
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