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15906Re: [EMHL] Thebault point

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  • Francois Rideau
    Dec 3, 2007
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      Dear Alexey
      Let T be the Thebault point and (L) the Euler line of ABC.
      The lines symmetric of (L) wrt the sides BC, CA, AB are on a same point U on
      the ABC-circumcircle.
      Then T is homothetic of U in the homothety of center G, the ABC-centroid and
      ratio -1/2.
      I think T is not on the ABC-Steiner inellipse.
      Friendly
      Francois

      On Dec 3, 2007 8:24 AM, Alexey.A.Zaslavsky <zasl@...> wrote:

      > Dear colleagues!
      > What is the number in ETC of Thebault point, i.e the common point of euler
      > lines of triangles AB'C', A'BC' and A'B'C where AA', BB', CC' are the
      > altitudes of ABC? Moscow scholar Fyodor Nilov asserts that this point is on
      > Steiner inellipse . Is this correct?
      >
      > Sincerely Alexey
      >
      > Antivirus scanning: Symantec Mail Security for SMTP.
      >
      > [Non-text portions of this message have been removed]
      >
      >
      >


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