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If you are trying to create a 'doughnut' effect then you can achieve the results with the Export Data function and select 'Inside.' This should perform the inverse clip that you are trying to create.
Per the Help,
Right click the layer in the table of contents and then convert it to graphics. Then be sure the graphic is selected and then you can use the Export Data workflow.
The "convert to graphics" option doesn't seem to be working for me. The "selected graphics" button is still grayed out, and the polygon layer is selected. Any ideas?
Mark,
To get rid of the graphics you created, just select them and hit the Delete key.
Eric
No problem Mark. I just didn't want you to keep having to start blank maps. Is there a reason why you're going through this 'convert to graphics' workflow rather than just hitting the Mask button on the Image Analysis Window? I mentioned this method well before Jeff S. replied to you -technically it was even before you posted the question. Maybe you didn't read the whole thread. You can also Clip with the Image Analysis window - all you need to do for both is select a polygon from your feature class. No conversion to graphics required.