You might like to read through this post and this post and the whole topic generally, but i guess the short answer is that there is no tool that will alllow you to do this in one shot.

Thank you druban for your thoughtful response. I have since been able to find two subroutines on the Internet, one written in Java and one in Visual Basic, which could be used to find a common tangent to two circles and a tangent to a circle through an external point (like the center of another circle, for example). I am wondering how difficult at this point it is to write an extension to Inkscape.

This example works with a common tangent to two circles:
(1) Essentially, a user would select one circle and one circle only.
(2) Next, the extension would get activated from a menu or hot key, and Inkscape would enter a mode.
(3) Then, a user would select another circle and a tangent line segment common to the two circles would appear.
There may be up to four of these, and the user could cycle between them.
(4) Press enter to select a tangent and repeat (3) and (4) with the second circle becoming the first circle in a new common tangent scenario.
(5) Finally, press escape when done to exit the mode.

In summary, I know now how to program in two types of tangents, but do not know how to write an Inkscape extension with the above features. The extension's mode, once entered into, would read Inkscape data but only utiilze a specialized subset of Inkscape's features, but would add its own features while in the mode. Is there a documented API for Inkscape? Is Python the language for the API/

By the way, I can't make up my mind between doing this project in Processing or Inkscape.