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Determining the Hole of a Doughnut

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Hey everybody,
just started with GIS and lots of problems to solve :confused:
I have a polygon with a hole in it like a doughnut. Now i would like to recieve a polygon with the shape of the hole. I tried to dissolve the polygon with no gaps allowed and then to clip the original from the dissolved one, but this did not work out.
I hope somebody can understand what i mean, my expression is horrible, sorry...
Can anybody help?
Thanks in advance!

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