Question 22
In rectangle $ABCD,$ we have $AB = 8,$ $BC = 9,$ $H$ is on $\overline{BC}$ with $BH = 6,$ $E$ is on $AD$ with $DE = 4,$ line $EC$ intersects line $AH$ at $G,$ and $F$ is on line $AD$ with $\overline{GF} \perp \overline{AF}.$ Find the length $\overline{GF}.$
