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22490Re: Generalization of P. Moses Circle (Re: Trilinear poles) [1 Attachment]

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  • Antreas Hatzipolakis
    Jul 2, 2014

      [APH]:
      Let (A), (B), (C) be three circles tangent all externally or internally
      a circle Q at A',B',C', resp.

      Denote:
      Ab = the inversion of A' in (B)
      Ac = the inversion of A' in (C)
      Bc = the inversion of B' in (C)
      Ba = the inversion of B' in (A)
      Ca = the inversion of C' in (A)
      Cb = the inversion of C' in (B)
      Ma = the midpoint of BaCa
      b = the midpoint of CbAb
      Mc = the midpoint of AcBc
      The lines AMa, BMb, CMc are concurrent ??

       
       
      [Peter Moses]:

      No
      Neither are lines AmA, BmB, CmC where
      mA = the midpoint of BcCb
      mB = the midpoint of CaAc
      mA = the midpoint of BaAb
      These were not calculated, but the external tangents case was drawn.
       
      Best regards,
      Peter.

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