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15396Re: [EMHL] Re:Cevian Trace Equal Area Points

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  • Francois Rideau
    Aug 2 6:38 AM
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      Dear Nikos and Tuan



      > > Two segments XY, X'Y' are on given two lines. To
      > > find the locus of Z such that Area(ZXY) =
      > > Area(ZX'Y').
      > > If areas are not signed then the locus is two
      > > lines passing intersection of two given lines.
      >
      > I note this fact:
      >
      > These 2 lines of this locus are harmonic conjugate wrt lines XY and X'Y'.


      So if abc and a'b'c' are 2 inscribed triangles in ABC and if we use ordinary
      area ( i.e not signed), the Tuan-Nikos six lines cut themselves in 4
      points forming an harmonic quad wrt ABC, each of these four points beeing an
      equal area center wrt abc and a'b'c'. I will have to think about it in
      choo-choo theory!
      friendly
      Francois

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