Hello, How about something like this:
annulus[point : {x_, y_}, radii : {ri_, ro_}, color_: Black] :=
Graphics[
GraphicsGroup[{color, Disk[point, ro], White, Disk[point, ri]}]
]
e.g.,
annulus[{1, 2}, {3, 5}]
annulus[{1, 6}, {4, 4.2}, Yellow]
This assumes that the background is white. You would need to use Show[] to combine it with other graphics. You could modify this to use limits for theta as well.
