Try this:
RegionDifference[Disk[{1, 0}, 1], Disk[{1.5`, 0}, 0.75`]];
R = DiscretizeRegion[%];
Graphics[{LightBlue, MeshPrimitives[R, 2], Orange, Circle[{1, 0}, 1],
Blue, Circle[{1.5`, 0}, 0.75`]}]
The MeshPrimitives will convert Discretized Regions into Graphics primitives.
You can get a handy little palette I did for the Geometry routines here:
Geometry Palette
