A participant in an online course just wrote me to ask how to construct an annulus (the region between two concentric circles). She tried constructing the interior of both circles and coloring the smaller one white, but found that the color of the larger interior bled through. This is expected: whether you can see one circle interior through the other depends on the layering and opacity of the two interiors. One solution is to choose Edit | Properties | Opacity to make the interior of the smaller circle 100% opaque (so that nothing shows through), and to be sure that the smaller circle is in front of the larger (by using the Context menu to bring the smaller to the front or send the larger to the back).

Alternatively, there's a nice locus construction that creates an annulus. First construct the two concentric circles AB and AC, where A is the common center. Then follow these steps:
  1. Construct point D on either circle.
  2. Construct ray AD.
  3. Construct the intersection E of ray AD with the other circle.
  4. Construct segment DE, and hide the ray.
  5. Select point D and segment DE and choose Construct | Locus.
The resulting locus probably has gaps in it. You can deal with these gaps in either or both of these ways:
(a) Select the locus and change its line style to Thick.
(b) Select the locus, choose Edit | Properties | Plot, and increase the number of samples to 1000 or so.