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More loci in the style of Antreas

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  • Darij Grinberg
    Given a point P in the plane of a triangle ABC, call P the complement of P, and A B C the cevian triangle of P . What is the locus of all P such that the
    Message 1 of 1 , Jan 31, 2004
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      Given a point P in the plane of a triangle ABC, call
      P' the complement of P, and A'B'C' the cevian triangle
      of P'. What is the locus of all P such that the

      (1a) parallels
      (1b) perpendiculars

      from A, B, C to the lines PA', PB', PC' concur?

      Variation: Let P' be the isotomic conjugate of P
      instead. Again, we have the locus of all P such that
      the

      (2a) parallels
      (2b) perpendiculars

      from A, B, C to the lines PA', PB', PC' concur.

      Both (1a) and (2a) loci are degenerated sextics
      consisting of the three medians of triangle ABC
      together with (the line at infinity)^3.

      Anybody to calculate (1b) and (2b)?

      Darij Grinberg
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