Michael,

here is a simple 2d drawing where I was trying to create the blue lines. For what I would call the "external" tangent lines, the solution is to create a circle inside the larger circle with a radius of R2-R1 then draw a line from the center of the small circle tangent to this circle we just created and translate this line to the edge of small circle (followind the perdendicular radius). Basically, it's the same for the "internal" tangent-tangent lines except this time you create a new circle with radius R1+R2.

I haven't tried any of this on curves yet maybe some day I'll have a need for it but my guess is it would be a little more complicated.

@bemfarmer: I got this idea from here http://mathworld.wolfram.com/Circle-CircleTangents.html

Thanks,
Felix