Hi Wimverbe,
MoI has a "Tan-Tan" snap which means the line is tangent to BOTH objects

Click your first circle (The approximation you mention) and navigate to the second circle.

You will then get a "Tan" snap.

If you move around in that area a bit, you will get a "Tan/Tan" snap, which adjusts the 2 pick points. Click that.

Your line is tangent to both circles.