Perfect Circle and Square

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The GIMP does not include standard tools to draw circles and rectangles, however you can draw these using selection tools and the fill tool. You can draw either a filled circle or rectangle or one that is outlined. The latter includes more step but the idea is same as drawing the filled shape.

The example below uses the circle, however you can use the rectangle tool to create squares as well.
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Step 1. Select either the rectangle or ellipse selection tool from the toolbox. If you want the shape to be anti-aliased, check the box labelled 'Anti-Aliased' in the Tools Options dialog. If you want the circle or rectangle to have fuzzy edges, you can adjust the 'Feature' values as well in the Tools Options dialog.
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Step 2. Draw the circle. If you want a perfect circle, hold down Shift, and then draw the circle. Once the circle is drawn, you will need to keep the selection active; otherwise you will not be able to fill it.
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Step 3. Now, we simply use the Fill Bucket tool, and click anywhere in the circle. Once this is done, you can remove the selection by right-clicking then choosing Select->None, or you can use the short-cut key Shift+Ctrl+A. If you want to make an outlined circle, see Step 4.
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Step 4. Doing an outlined circle is simple, after step #3, right-click, then choose Select->Shrink. You will be presented with a dialog (see below) that will allow you to specify how many pixels you want to shrink the selection by. Choose 1 and click OK. Once the selection has shrunk, you will need to delete the interior by right-clicking, then choosing Edit->Clear. Or you can use the short-cut key Ctrl+K.
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This box lets you specify how many pixels you want to shrink the active selection by.