9830Re: [EMHL] The Brocard points of a quadrilateral (Geoff Millin)
- Jun 1, 2004Darij raised some interesting questions about harmonic quadrilaterals.
> I don't see, however, any formula of the kindCasey, 'A sequel to Euclid', has various theorems on harmonic n-gons,
> cot w = cot A + cot B + cot C for the Brocard
> angle of a harmonic quadrilateral.
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.
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