Venn diagrams in Visio?

Logic texts use simple diagrams called Venn diagrams. They have
overlapping circles as components, with parts of the circles filled
in, to illustrate different relations between sets.

If I put two overlapping circles on a Visio diagram, I can fill in
both circles with the same pattern. This illustrates the union of two
sets.

To illustrate the intersection, I need to fill in just the area where
the two circles overlap. This area is not a separate Visio shape, so
I'm having trouble figuring out how to do this. I thought maybe I
could give complementary fills to the two circles somehow, so that the
fill would only be visible in the intersection, but haven't found
anything that works.

Anybody know a Visio trick to solve this problem?

Thanks.

Mike Carroll