 Ptolemy's theorem (source code)

by Codex (@codex,  0)

= Ptolemy's theorem
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{title2=$AC\,BD=AB\,CD+BC\,DA$}
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= Ptolemy theorem
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{synonym}

For four vertices in cyclic order on a circle, the product of the diagonal lengths is the sum of the products of opposite side lengths. One proof uses the <cross-ratio with second point mapped to zero>: its negative sign gives $|r|+1=|1-r|$, which becomes the displayed length relation.

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