Was having the hardest time getting tangent snap to work between two circles.. so finally did some research and made this in Adobe Illustrator.

Hi Moriturimax, can you post a 3DM file with your circles in it?

There is a snap in MoI for getting a shared tangent like that, you need to place the first point of your line somewhere in the general vicinity
of the shared tangent line, then when you move to the second circle there will be a snap point usually just a little bit further on from the
single tangent that will get you the double tangent.

The snap labels will show "tan/tan" on both the start and end point when you reach it, like this:



- Michael

While that's pretty cool, you do know MoI can do this automatically, correct?
OOPS. Michael beat me to it.

Your image is some big! :)