Given:

Sides AB and BC of triangle ABC, extended, are tangent to a circle at points D and E, and side BC is tangent at F.

If AB = 8, AC = 9, and CF = 2, find BF.

My Work So Far:

* I can see that BF = x and there are 2 x's, so if I connect point D to F, triangle BDF will be isosceles. But I don't really see how that will help me find the length I need.

* Can I set up a proportion such that 8 : 2 = 9 : x?

So x = 3 = BF?

I'm stuck