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10974Re: [EMHL] circumcevian reflections

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  • Bernard Gibert
    Jan 5, 2005
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      Dear Floor and friends,

      may I wish all the best to all of you for this new year.

      > [FvL]To start the new year let me offer a little theorem:
      >
      > If A'B'C' is a circumcevian triangle [of point P], and A"B"C" are the
      > reflections of
      > A'B'C' through the sides of ABC, then the circles (ABC), (A"B"C),
      > (A"BC")
      > and (AB"C") are concurrent in one point.

      your point is the isogonal conjugate of the infinite point of the
      direction which is perpendicular to HP.

      notice that ABC and A"B"C" are perspective iff P lies on the Jerabek
      hyperbola or at infinity.

      Best regards

      Bernard

      [Non-text portions of this message have been removed]
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