A circle within a circle - How to make the center transparent?

Let's say I create a circle and then a smaller circle within the larger one.  How can I make the center of the circle transparent so that when it is over other objects only the center of the object will allow what is beneath to show through?

 Transparency can't do it from what I can see since you can make the center (smaller circle) transparent but if you make the larger one transparent then you can't have the resulting object a color.

 I could use the eraser tool on both circles in the center but that seems tedious.

 I want to make other more complex objects with "holes" in them but can't figure out an easy way to do it.

Thanks,

 Mark