If I understood your question correct, with the help of google translator
I want to draw a segment with the following constraints:
- known length
- one end on a circle
- The other end on another circle
I got this solution:
Make a copy of the left circle, by the known distance to the right side, to get the red circle.
Make a copy of the right circle, by the known distance to the left side, to get the green circle.
Use the command line for exact distance, e.g. move reference 0,0, move to 20,0 or -20,0.
Use the intersection snap tool to draw the magenta line.
This line is horizontal, with a length of the known distance.
Then you can delete the red and green circles, done