Mathematics IV: circles

[True Federalist (진정한 연방 주의자)]

Assuming by "touch" you mean "tangent", then one, assuming you have Euclidean geometry in play.  You'd be able to get a second circle to do that in those non-Euclidean geometries where circles and straight lines are simply two different ways of expressing the same object.

[True Federalist (진정한 연방 주의자)]

More importantly, we can now conclude that two important differences exist between angus polls and excelsus polls.

Exactly. But I don't use this option out of spite, but rather for reasons of impartiality.

then that's another issue entirely.  You clearly drew a line segment.  You then, after folks voted--in a poll in which you did not allow users to change their votes!--made it clear that you actually intended to make it a line instead of a line segment.  By this we are left to conclude that you are either (a) too ignorant to use the accepted and customary symbols for denoting lines, rays, and line segments, or (b) you are a troll and a trickster.

What terms do you use for lines with (a) no endings, (b) two endings and (c) one beginning and no end?
For the latter I guess "ray". I'd call it half-line.

No ending is "line"
One ending is "ray"
Two endings is "line segment"

[True Federalist (진정한 연방 주의자)]

Or we could have been missing the point and its really a grammar problem rather than a math problem.  He asked for circles touching each of the objects, not circles touching all of the object.

For each of the objects there are an infinite number of such circles that touch each individual circle or line without intersecting any of the three.