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Re: Concurrent circles problem

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  • yiuatfauedu
    Dear Antreas, [APH]: Let ABC be a triangle, P a point and A ,B ,C the circumcenters of PBC,PCA,PAB, resp. The circumcircles of AB C , BC A , CA B concur on
    Message 1 of 2 , Mar 26 8:30 AM
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      Dear Antreas,

      [APH]: Let ABC be a triangle, P a point and A',B',C' the
      circumcenters of PBC,PCA,PAB, resp.
      The circumcircles of AB'C', BC'A', CA'B'
      concur on the circumcircle of ABC, at a point, name it dP,

      Which are the coordinates of dP ?
      (they are somewhere in Hyacinthos, but where?)

      For P = O, H we have dO = dH.

      Which other isogonal conjugate points P,P*
      have the same property (locus of P)?

      In general, for which points P,Q we have dP = dQ ?

      *** If P is not on the circumcircle, this common point dP is
      the antipode of the isogonal conjugate of the infinite point of the line PP*. Equivalently, it is the perspector of the triangle bounded by the reflections of PP* in the sidelines.

      Best regards
      Sincerely
      Paul
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