USAMO 1994 Problem 3

The hexagon $\mathrm{ABCDEF}$ has the following properties: (1) its vertices lie on a circle; (2) $\mathrm{AB}=\mathrm{CD}=\mathrm{EF}$; and (3) the diagonals $\mathrm{AD}, \mathrm{BE}, \mathrm{CF}$ meet at a point. Let $\mathrm{X}$ be the intersection of $\mathrm{AD}$ and $\mathrm{CE}$. Show that $\mathrm{CX} / \mathrm{XE}=$ $(\mathrm{AC} / \mathrm{CE})^{2}$.