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9145Re: [EMHL] Re: excircle and circumcircle

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  • Alexey.A.Zaslavsky
    Jan 28, 2004
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      Dear Darij!
      >The equivalence of the conditions 2. and 5. was the
      >subject of Problem 4 in the Bundeswettbewerb
      >Mathematik (German National Mathematics Olympiad)
      >2002, 2 round. In fact, it was a very hard problem;
      >I was lucky enough to know the method of trilinear
      >coordinates to solve it!

      The equivalence of 2 and 5 is a particular case of next fact. Let given a
      triangle ABC and a point P. A1, B1 are the common point of AP and BC, BP and
      AC. Q - a point in A1B1, Q' is isogonally conjugated to Q, A2, B2 are the
      common points of AQ' and BC, BQ' and AC. Then the point P' isogonally
      conjugated to P is in A2B2. This can be easily proved by trilinear

      Sincerely Alexey
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