In $$\triangle ABC$$, $$AB=6$$, $$BC=7$$ and $$CA=8$$. Point $$D$$ lies on $$BC$$ and $$AD$$ bisects $$\angle BAC$$. Point $$E$$ lies on $$AC$$ and $$BE$$ bisects $$\angle ABC$$. If the bisectors intersect at $$F$$, then the ratio $$AF:FD$$ is

By the angle bisector theorem, $$BD:DC=AB:AC=6:8=3:4$$. Since $$BC=7$$, we get $$BD=3$$. Applying the angle bisector theorem again in triangle $$ABD$$ gives $$AF:FD=AB:BD=6:3=2:1$$. Under the numeric-only TITA rule, the answer field is recorded as $$2$$, while the explanation preserves the required ratio.