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9830Re: [EMHL] The Brocard points of a quadrilateral (Geoff Millin)

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  • dick tahta
    Jun 1, 2004
      Darij raised some interesting questions about harmonic quadrilaterals.

      > I don't see, however, any formula of the kind
      > cot w = cot A + cot B + cot C for the Brocard
      > angle of a harmonic quadrilateral.

      Casey, 'A sequel to Euclid', has various theorems on harmonic n-gons,
      including a formula for the Bocard angle ascribed to Tucker, namely:
      cosec^w = cosec^A + cosec^B + ....

      Casey also gives the result (for n=4) about equal products of opposite
      sides. It is also in Johnson's Advanced Euclidean Geometry' (Th 133) which
      also quotes (Th504) further Brocard properties ascribed to Tucker.

      Dick Tahta
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