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Re: Equal cevians

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  • Francisco Javier
    Dear Nikolaos, These special cases are also cited in article by Pounder cited in Hyacinthos message #21039. Best regards, Francisco Javier.
    Message 1 of 5 , Sep 21, 2012
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      Dear Nikolaos,

      These special cases are also cited in article by Pounder cited in Hyacinthos message #21039.

      Best regards,

      Francisco Javier.

      --- In Hyacinthos@yahoogroups.com, Nikolaos Dergiades <ndergiades@...> wrote:
      >
      > Dear friends
      >
      > If A'B'C' is the cevian triangle of a point P
      > and AA' = BB' = CC' then the points P are
      > the foci of Steiner circumellipse (Bickart points),
      > the intersections of circle A(a) with BC,
      > the intersections of circle B(b) with CA,
      > the intersections of circle C(c) with AB,
      > that is at most 8 points. Is it correct?
      >
      > Best regards
      > Nikos Dergiades
      >
    • Nikolaos Dergiades
      Dear Francisco, ... thank you very much. By the way Can you help me for the following equation? a^7 b^2 - 3 a^5 b^4 - a^4 b^5 + 2 a^3 b^6 + a^2 b^7 - a^7 b c -
      Message 2 of 5 , Sep 21, 2012
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        Dear Francisco,

        > These special cases are also cited in article by Pounder
        > cited in Hyacinthos message #21039.

        thank you very much.
        By the way
        Can you help me for the following equation?

        a^7 b^2 - 3 a^5 b^4 - a^4 b^5 + 2 a^3 b^6 + a^2 b^7 - a^7 b c -
        a^6 b^2 c + 4 a^5 b^3 c + 2 a^4 b^4 c - 4 a^3 b^5 c - 3 a^2 b^6 c -
        a b^7 c + a^7 c^2 - 3 a^6 b c^2 + 7 a^4 b^3 c^2 + 7 a^3 b^4 c^2 -
        a b^6 c^2 + b^7 c^2 + 2 a^6 c^3 - 4 a^5 b c^3 + 7 a^4 b^2 c^3 -
        33 a^3 b^3 c^3 + 7 a^2 b^4 c^3 + 4 a b^5 c^3 - a^5 c^4 +
        2 a^4 b c^4 + 7 a^3 b^2 c^4 + 7 a^2 b^3 c^4 + 2 a b^4 c^4 -
        3 b^5 c^4 - 3 a^4 c^5 + 4 a^3 b c^5 - 4 a b^3 c^5 - b^4 c^5 -
        a^2 b c^6 - 3 a b^2 c^6 + 2 b^3 c^6 + a^2 c^7 - a b c^7 + b^2 c^7 = 0

        If a,b,c are triangle sides does it hold only for a = b = c ?

        Best regards
        Nikos Dergiades
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