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A perspector in Conway configuration

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  • Atul Dixit
    Dear all I suppose this is already known. Let ABC be a triangle.Consider the Conway configuration(configuration of Conway circle)i.e On sides AB and AC,past
    Message 1 of 1 , Dec 31, 2001
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      Dear all
      I suppose this is already known.
      Let ABC be a triangle.Consider the Conway configuration(configuration of
      Conway circle)i.e On sides AB and AC,past A,consider points P1 and P2
      respectively such that AP1 = AP2.Similarly construct points P3,P4(on BC and
      AC respectively) and P5 and P6(on AB and BC respectively).
      Let P12 = P1P3/\P2P6 and P45 = P3P5/\P4P6
      (P12 , P45 are on the either sides of A)
      Similarly P56 = P1P5/\P4P6 and P23 = P1P3/\P2P4
      and P34 = P2P4/\P3P5 and P16 = P2P6/\P1P5
      Then line P12P45 passes through A and similarly lines P56P23 passes
      through B and line P34P16 passes through C.
      Thus triangles P12P34P56 and P45P23P16 are perspective with ABC at
      same point.
      I suppose there are many more things to investigate in this
      configuration.

      Happy new year
      Yours faithfully
      Atul.A.Dixit



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