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diagonals' concurrency criterion in a cyclic hexagon

Source: Switzerland - Swiss MO 2008 p8

July 17, 2020
geometryhexagonCyclicconcurrencyconcurrentdiagonals

Problem Statement

Let ABCDEFABCDEF be a convex hexagon inscribed in a circle . Prove that the diagonals AD,BEAD, BE and CFCF intersect at one point if and only if ABBC⋅CDDE⋅EFFA=1\frac{AB}{BC} \cdot \frac{CD}{DE}\cdot \frac{EF}{FA}=1
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