### Theory:

The possible variants of positioning the two circles in a common point.

1. The circles have no common points, and they are off each other.

2. The circles have no common points, and they are inside each other.

3. The circles have one common point, touching them externally.

4. The circles have one common point ($$B$$), and they touch internally.

5. The circles have two points in common, they intersect. Points $$I$$ and $$J$$ are common points and belong to both circles.
6. The circles have no common points, and their centers coincide, they are concentric.