Question 166
Let $ABCD$ be a square, and let $E$ be an internal point on side $AD$. Let $F$ be the foot of the perpendicular from $B$ to $CE$. Suppose $G$ is a point such that $BG = FG$, and the line through $G$ parallel to $BC$ passes through the midpoint of $EF$. Prove that $AC \lt 2 \cdot FG$.