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How to merge a radius to two circles tangently?

I am working on modeling this simple image below just as practice. I'm using SW 2013. The problem I am having is I cannot get the two radius' (the 42mm and 96mm) to terminate tangently(sp?) into the two circles (52mm and 36mm) as pictured.

I originally made two circles with a radius of 42mm and 96mm. I then selected the one of existing circles (52mm and 36mm) and the new circles, then added a tangent relation. The circles snapped into place. I then used power trim to get rid of the parts of the circles I no longer needed. Now I get an error message because even though the circles are tangent, when I zoom in tight, there is a very small gap.

When I merge the two circles without trimming, I can zoom all the way in and see that the circles overlap a small amount, causing its own error.