You can put this solution on YOUR website! Searching for dct to two circles, I found it to stand for "direct common tangent",
and I found that phrase to mean tangent common to both circles that does not cross the line connecting the circles' centers between the centers.
There is two of those, of course,
and they remind you of a belt wrapped around two pulleys.
I found that indirect common tangents would be the ones that cross between the circles.
CIRCLES (with the line connecting their centers:
Drawing that with pencil, ruler, and compass,
and adding the direct common tangents with a straightedge or ruler would be easy.
Calculating coordinates for the points of tangency is not so easy.
Here is the drawing with the direct common tangents added.
CIRCLES (with the line connecting their centers:
