I have a line from A to B and a circle positioned at C with the radius R.
What is a good alg
If you find the distance between the center of the sphere (since it's 3D I assume you mean sphere and not circle) and the line, then check if that distance is less than the radius that will do the trick.
The collision point is obviously the closest point between the line and the sphere (which will be calculated when you're calculating the distance between the sphere and the line)
Distance between a point and a line:
http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html