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[Flunkie]

Alright, so this problem has me stumped. Everything that looks tangent is tangent and everything that looks the way it is, it probably is. I need to know the steps used to solve it. I asked around and got that the answer is either 6 or 1.5, but I still need the steps.

Bigger image: http://i43.tinypic.com/i36jx4.jpg

If you can help, thanks!

 

[Therion]

Label the point where the circles touch K. Then right triangle CGD is similar to FKD. CD and CG give you DG. Then use the similarity to find FD and FG.
That makes sense to me, but it doesn't get me 6 or 1.5, so I might have it wrong.

Edit: Actually, I must be misinterpreting the diagram somewhere, because the numbers just don't work out. DGC should be a 3-4-5 right triangle, similar to DEA, a 15-8-17 right triangle. But they aren't similar, so I'm guessing a line I think is tangent isn't really.

Looking at it again, I think the diagram must just be wrong. If CD=5 and the circle has radius 4, then that long bit outside the circle is 1. That's just not going to happen with circles of those radii. If those were diameters it might work out.

 

[MarzipaNMOS]

i wuz bored

there might be an easier way

 

[Therion]

12 is the answer I get using the method I described. But I still think the problem has an impossible configuration, so you should be able to get a conflicting answer by doing it differently. Using the bigger similar triangle, EG = 12, so FG can't be 12 unless E = F.