Another method.
1. Create the overlapping circles.
2. Select a circle (we will call this circle 1) by Ctrl+click on its layer in the layers palette. You should have 'marching ants' around the perimeter of circle 1.
3. Click on overlapping circle (circle 2) in the layers palette.
4. Layer>New>Layer via copy. This will create a new shape out of the overlapping area.
5. Repeat this process with circles 2 and 3 and again with 1 and 3. Then one more time with the overlap of two of the 'cut out' portions to get the center section.
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