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8752Two Emile Hyacinthe Lemoine centers

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  • jpehrmfr
    Dec 1, 2003
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      Dear Hyacinthists
      looking at the beginning of the very interesting from EH Lemoyne :
      Suite de theoremes et de resultats concernant la geometrie du
      triangle
      avalaible at
      http://www.hti.umich.edu/u/umhistmath/
      I see that he discovered the following centers :
      1) Ma is the unique point on the segment BC such as
      MaB + d(Ma,AB) = MaC + d(Ma, AC) with d for distance; define Mb, Mc
      cyclically. Then MaMbMc and ABC are perspective at the point of the
      line IG with trilinear 1+2R/a:...
      2) Na is the unique point on the segment BC such as
      NaB + d(Na,AC) = NaC + d(Na, AB) with d for distance; define Nb, Nc
      cyclically. Then NaNbNc and ABC are perspective at the point of the
      line IG with trilinear (2R/a)-1:...
      I don't think - but, may be, I'm wrong - that these points are in
      the current ETC.
      Friendly. Jean-Pierre
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