When you create images and objects in GIMP, one of your more powerful options is the Paths tool. However, while this tool is great for a number of shapes, such as polygons and lines, it's not always ...
In the Gimp, you should be able to simply use the elliptical selection tool (E) to select the area you want, and then either copy and paste into another image, or Select->Invert (Ctrl+I) and then Edit ...
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