On a necessary and sufficient cyclicity condition for a quadrilateral

S. Yu. Sadov


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.