Not sure, thought of everything from finding the length of the transverse common tangent of the circles, to staring at the Inscribed Angle Theorem for a while...
The Attempt at a Solution
I believe I'm overthinking this problem, at first I tried to find a way of figuring out the slope of the transverse common tangent, but the figures aren't on a coordinate plane, so I'm not sure how I would go about it, or even if that's needed to solve the problem.
Then I gave some thought to finding the radii of the two circles based off the length of the inner tangent, which is given as 5 inches, though I'm not sure how that would help either.
I suppose I just need a hint in the right direction, this seems so simple, but for some reason the solution just isn't clicking.