Almost any decent drawing program can be used to produce a geometric figure.
What makes dynamic geometry programs different is that they understand the
fundamental concept of incidence, and of how one object may depend on others.
Thus, if one part of a figure is moved, then all parts dependent on that also move.
There are many programs available, and I have tried most of them. I generally use
either Cabri (with CabriJava for publishing to the Web) or Cinderella, which has this
facility built in. Cabri (£100) and Cinderella (£40) are commercial, while some of the
others are free. I reckon that most of the free ones are just about value for money.