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Re: Fwd: About a problem quoted in Hyacinthus

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  • patrickmorton289
    Dear Francisco, I believe I have a synthetic proof of the theorem you mention. Is the MT point associated to P the complement of the isotomic conjugate of P?
    Message 1 of 2 , Oct 25, 2012
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      Dear Francisco,

      I believe I have a synthetic proof of the theorem you mention. Is the MT point associated to P the complement of the isotomic conjugate of P? This has been called the "isotom-complement" by Grinberg.

      If the answer to this question is yes, then I have such a proof, which I found several years ago with my student Igor Minevich.

      Patrick Morton


      --- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis <anopolis72@...> wrote:
      >
      > ---------- Forwarded message ----------
      > From: Francisco Bellot Rosado <franciscobellot@...>
      > Date: Wed, Oct 24, 2012 at 11:08 AM
      > Subject: About a problem quoted in Hyacinthus
      > To: anopolis72@...
      >
      >
      > Dear Prof. Hatzipolakis,
      > my name is Francisco Bellot and I am very interested in a very nice
      > problem, partly quoted in the message of Hyacinthus #18776, dated
      > March 30, 2010:
      > "When points are cyclocevian conjugates, their MT (Miquel associated
      > points) are isogonal conjugates".
      > I know a proof with barycentric coordinates, but I wonder if there is
      > also a synthetic proof and, moreover, the origin of this problem. I
      > think it would be known by the french geometers of the XIX Century,
      > but my search on it (FGM, Mathesis, etc) have been unsuccesful. I
      > would be very grateful to you if you can help me on this problem.
      > Best regards,
      > Francisco
      >
      > --
      > Francisco Bellot
      > Europe representative of the World Federation of National Maths Competitions
      > Editor, Digital journal REOIM (Revista Escolar de la Olimpiada
      > Iberoamericana de Matemática)
      >
      >
      > --
      >
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