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Re: [EMHL] quadrilateral problem

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  • abogom
    ... I happen to have a Russian edition of the book edited by D. I. Perepyolkin, who also supplied solutions to all the exercises. For #421 he makes a reference
    Message 1 of 4 , Jan 12, 2004
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      Dear Darij:

      > This last part is nice. I was too lazy to check
      > this with my dynamic program, but let me cite a
      > related problem from Hadamard: nr. 421 from his
      > "Lecons de Geometrie Elementaire", tome 1,
      > stating that
      >
      > circumradius of Ai'Bi'Ci'Di' a + c - b - d
      > ---------------------------- = -------------,
      > circumradius of Ae'Be'Ce'De' a + c + b + d
      >
      > where a, b, c, d are the sidelengths of the
      > quadrilateral ABCD.
      >
      > I have not been able to prove this fact, but,
      > of course, it generalizes the well-known
      > theorem that the quadrilateral ABCD has an
      > incircle if and only if a + c = b + d.

      I happen to have a Russian edition of the book edited by D. I.
      Perepyolkin, who also supplied solutions to all the exercises. For
      #421 he makes a reference to #362a. If you want I can scan for you
      both solutions.

      All the best,
      Alex
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