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Collinearity of first trisection points of cevian segments

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  • yiu@fau.edu
    Dear friends, Happy New Year! It is well known that the midpoints of the three cevian segments of a point are never collinear. What is the locus of P for which
    Message 1 of 2 , Jan 1, 2001
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      Dear friends,

      Happy New Year!
      It is well known that the midpoints of the three cevian
      segments of a point are never collinear. What is the locus of
      P for which the ``first'' trisection points of the three cevian
      segments (the ones nearer to the vertices) are collinear?

      Best regards.
      Sincerely,
      Paul
    • Francisco Javier
      This question was forgotten for too long! The locus is line at infinity + Steiner circumellipse. When the point is on the Steiner circumellipse, the line
      Message 2 of 2 , Oct 23, 2011
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        This question was forgotten for too long!

        The locus is line at infinity + Steiner circumellipse. When the point is on the Steiner circumellipse, the line through the three division points goes trough the centroid.

        Best regards,

        Francisco Javier.

        --- In Hyacinthos@yahoogroups.com, yiu@... wrote:
        >
        > Dear friends,
        >
        > Happy New Year!
        > It is well known that the midpoints of the three cevian
        > segments of a point are never collinear. What is the locus of
        > P for which the ``first'' trisection points of the three cevian
        > segments (the ones nearer to the vertices) are collinear?
        >
        > Best regards.
        > Sincerely,
        > Paul
        >
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