Geometry Level 4

In $$\Delta ABC$$ ,$$AD , BE , CF$$ are concurrent such that $$D,E,F$$ are points on $$BC,AC,AB$$ respectively.

If $$CE=1$$ ,$$CD=2$$ ,$$BD=3$$ ,$$AF=4$$ ,$$AE=6$$ ,then what is the length of $$BF$$?

Note: Figure not to scale.

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