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The top layer has a drop shadow, but the shadow should not have any effect on the transparent area outside of the circle.
I tried using duplicating the circle and using Path-->Intersection, but that didn't clip the shadow.
Using Object-->Clip-->Set and Object-->Mask-->Set remove the shadow entirely, though there may be some setting that could allow them to work that I am unaware of.
In Inkscape, filter effects like a drop shadow can be clipped by adding the filtered object to a group first, then clip the group.
Tutorial
The end result in an object in which the drop shadow has been clipped!
Adding the green circle to the group is actually optional: a group with only the white shape could also be clipped. However that could result in small render artifacts at the bottom of the object.
