In \triangle A B C, A B=6, B C=7, and C A=8. Point D lies on \overline{B C}, and \overline{A D} bisects \angle B A C. Point E lies on \overline{A C}, and \overline{B E} bisects \angle A B C. The bisectors intersect at F. What is the ratio A F: F D ?
Answer Choices
A. 3: 2
B. 5: 3
C. 2: 1
D. 7: 3
E. 5: 2