How to create the shape of two circles connected by tangent lines in Carbide Create?

You would need to do the trigonometry to determine the tangents, or the necessary rotation.

I worked up an example of doing this in BlockSCAD here:

the file could be exported to OpenSCAD and a projection() command added to get a flat version which can be exported to a DXF or SVG.

Alternately, program in a tool such as Nodebox and export an SVG?