You could note: .
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
Thank you! I did some research, and wow, had I known the fact that "2 tangents drawn to a circle from a point outside the circle are equal." then I would have gotten it right away. But I clearly don't remember our professor teaching that. Quite frustrating how they expect us to know something that wasn't taught: and we're paying for this kind of "education".
Anyway, thank you very much!!!