Mathematics IV: circles

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In the picture below, the two circles and the straight line are all tangent to each other.
How many circles exist that "touch" (not intersect!!!) each of the three objects?

Caution: The straight line doesn't have any ends.

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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.

Don't make it too complicated.
I'm only referring to the simple Euclidean geometry that every student learns at school.

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Definitely a freedom post, angus, but ...

I'm sorry to say your answer is wrong. 



Straight lines don't have endings.

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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.

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Butafly got it right. Period.