Adding Shapes/Images to a Map?

Is it possible to add a shape to a map, and in a way that the shape either moves with the map, or the map is locked in location?  Here is what I would like to do:

I have a large list of Lattitude and Longitudes to place on a map.  I want to be able to draw circles around certain areas to label them.  Example:  All the lat/longs in one circle are "area 1", all lat/longs in another area are "area 2", etc.

I see I can add basic shapes over top of a map, but every time the map is moved by a user (zoomed in/out, etc), the circle defining that area doesn't move.

Thanks.