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Fwd: About a problem quoted in Hyacinthus

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  • Antreas Hatzipolakis
    ... From: Francisco Bellot Rosado Date: Wed, Oct 24, 2012 at 11:08 AM Subject: About a problem quoted in Hyacinthus To:
    Message 1 of 2 , Oct 24, 2012
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      ---------- 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)


      --
    • 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 2 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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