IrMO 1988 Problem 6

The triangles $ABG$ and $AEF$ are in the same plane. Between them the following conditions hold: (a) $E$ is the mid-point of $AB$ ; (b) points $A,G$ and $F$ are on the same line; (c) there is a point $C$ at which $BG$ and $EF$ intersect; (d) $|CE|=1$ and $|AC|=|AE|=|FG|$ . Show that if $|AG|=x$ , then $|AB|=x^3$ .