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Unsolved Challenge Geometry Challenge

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MHB POTW Director
Staff member
Feb 14, 2012
The $\triangle ABC$ and $\triangle AEF$ are in the same plane. Between them, the following conditions hold:

1. The midpoint of $AB$ is $E$.
2. The points $A,\,G$ and $F$ are on the same line.
3. There is a point $C$ at which $BG$ and $EF$ intersect.
4. $CE=1$ and $AC=AE=FG$.

Prove that if $AG=x$, then $AB=x^3$.