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On a necessary and sufficient cyclicity condition for a quadrilateral

Sergey Sadov
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Abstract

A convex quadrilateral with sides a,b,c,d, and diagonals p,q is cyclic iff abp-bcq+cdp-daq=0. This condition, in spite of its simplicity, appears to be unnoted and unexpectedly proof-resilient. We employ advanced methods of computer algebra and nonlinear analysis.

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Sergey Sadov. 2004-10-08. On a necessary and sufficient cyclicity condition for a quadrilateral. https://arxiv.org/abs/math/0410234

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