Question 94
Let $ABCDEF$ be a convex hexagon with a circumcircle. Prove that the diagonals $AD$, $BE$ and $CF$ meet in a single point if and only if
$$
\frac{AB}{BC} \cdot \frac{CD}{DE} \cdot \frac{EF}{FA}=1
$$
$$
\frac{AB}{BC} \cdot \frac{CD}{DE} \cdot \frac{EF}{FA}=1
$$