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Two perspective triangles, developpment to new centers?

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  • Jean-Louis Ayme
    Dear Hyacinthists, 1. ABC a triangle, 2. A’B’C’ the médial triangle of ABC 3. M and N two antigonal points wrt ABC 4. PQR the homothetic triangle of
    Message 1 of 2 , Aug 30, 2011
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      Dear Hyacinthists,
      1. ABC a triangle,
      2. A’B’C’ the médial triangle of ABC
      3. M and N two antigonal points wrt ABC
      4. PQR the homothetic triangle of A’B’C’ with centre N and ratio 2
      5. A”B”C” the antipedal triangle of ABC wrt M (PA perpendicular to B”C” and so on)
      More generally, we can consider the anti isogonic triangle so that <PAB” and so on are all egal…
      Conclusion : A”B”C” and PQR are perspective.
      Application to pair of antigonal points centers?
      Sincerely
      Jean-Louis

      [Non-text portions of this message have been removed]
    • Jean-Louis Ayme
      Dear Hyacinthists, 1. ABC a triangle, 2. A’B’C’ the médial triangle of ABC 3. M and N two antigonal points wrt ABC 4. PQR the homothetic triangle of
      Message 2 of 2 , Aug 30, 2011
      View Source
      • 0 Attachment
        Dear Hyacinthists,
        1. ABC a triangle,
        2. A’B’C’ the médial triangle of ABC
        3. M and N two antigonal points wrt ABC
        4. PQR the homothetic triangle of A’B’C’ with centre N and ratio 2
        5. A”B”C” the antipedal triangle of ABC wrt M (PA perpendicular to B”C” and so on)
        More generally, we can consider the anti isogonic triangle so that <PAB” and so on are all egal…
        Conclusion : A”B”C” and PQR are perspective.
        Application to pair of antigonal points centers?
        Sincerely
        Jean-Louis

        [Non-text portions of this message have been removed]
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