Problem

Source: Switzerland - Swiss MO 2008 p8

Tags: geometry, hexagon, Cyclic, concurrency, concurrent, diagonals



Let $ABCDEF$ be a convex hexagon inscribed in a circle . Prove that the diagonals $AD, BE$ and $CF$ intersect at one point if and only if $$\frac{AB}{BC} \cdot \frac{CD}{DE}\cdot \frac{EF}{FA}=1$$