imc

$\angle GHC=\angle AHB$ (Vertical angles are equal). $\angle F=\angle B$ (Both are 90 degrees). $\angle BHA=\angle HAD$ (Alt. Interior Angles are congruent). Therefore $△GFA$ and $△ABH$ are similar. $△GCH$ and $△GEA$ are also similar. $DA$ is 9, therefore $EA$ must equal 5. Similarly, $CH$ must equal 3. Because $GCH$ and $GEA$ are similar, the ratio of $CH=3$ and $EA=5$, must also hold true for $GH$ and $HA$. $\frac{GH}{GA}=\frac{3}{5}$, so $HA$ is $\frac{2}{5}$ of $GA$. By Pythagorean theorem, $(HA{)}^2=(HB{)}^2+(BA{)}^2...HA=10$. $HA=10=\frac{2}{5}\ast (GA)$. $GA=25.$ So $\frac{GA}{HA}=\frac{GF}{BA}$. $\frac{25}{10}=\frac{GF}{8}$. Therefore $GF=\boxed{20}$.