I'm using the pen tool in CS5 to draw shapes, and I'm getting more comfortable with it, but one thing I'd really like to be able to do is add to a path. For example, if I draw a circle, I'd like to be able to bisect it with the pen tool and have two distinct paths emerge without having to draw two separate paths and try to get the duplicate points on top of each other by hand.
How do I do this?