In rectangle A B C D, we have A B=8, B C=9, H is on \overline{B C} with B H=6, E is on A D with D E=4, line E C intersects line A H at G, and F is on line A D with \overline{G F} \perp \overline{A F}. Find the length \overline{G F}.
Answer Choices
A. 16
B. 20
C. 24
D. 28
E. 30