You may be asked to show that two circles are touching, and say whether they're touching internally or externally. To do this, you need to work out the radius and the centre of each circle.

The only way to do this is to have the second circle intersect the first at two points (touching at only one point would result in only three regions: first set, second set or neither).

I proceeded into the intersection, much to her dismay. She honked and screamed at me and was very ugly about the whole thing. "I assume the reader is inquiring about neighborhood traffic circles ...