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Re: [EMHL] Thomson's cubic

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  • jean-pierre.ehrmann@wanadoo.fr
    Dear Antreas, Bernard, Edward and other Hyacinthists, [APH] ... of ABC ... If you note that an pivotal isogonal cubic wrt the antimedial triangle goes through
    Message 1 of 4 , Oct 31, 2001
      Dear Antreas, Bernard, Edward and other Hyacinthists,

      [APH]
      > There should be a general theorem saying what cubic of ABC
      > is a given (pivotal) isogonal cubic of its antimedial triangle.
      >
      > Is it always true that an isogonal cubic of the antimedial triangle
      of ABC
      > is an isotomic cubic of ABC? (as in the above case)

      If you note that an pivotal isogonal cubic wrt the antimedial
      triangle goes through ABC iff the pivot is the centroid, the above
      case is the only possible one.

      A kind of generalization could be the following :
      f is an isoconjugation wrt the precevian triangle of P
      g is the isoconjugation wrt ABC with P as fixed point
      Then
      M, f(M), P lie on a same line iff
      M, g(M), f(P) lie on a same line
      Friendly. Jean-Pierre
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