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While this tool is normally creating an ellipse-shaped selection, you can use it to create circles as well. You'll find this tool in the upper-left corner of the Toolbox window. Click and drag on your canvas to begin creating an ellipse shape. ⇧ Shift after you start dragging to create a circle. This will snap the ellipse into a perfect circle shape. Make sure to keep holding ⇧ Shift as you release your mouse button. If this doesn't work properly the first time, try starting a new ellipse. You can specify the exact size of the circle by using the "Size" fields in the "Tool Options" section of the Toolbox. Make sure the height and width are the same to make a perfect circle. Click the foreground color box in the Toolbox to open the color picker. This color will fill the circle. The circle will be borderless. The circle will fill with the color you selected.

Summary:
Click the Ellipse Select Tool in the Toolbox. Start creating an ellipse by clicking and dragging. Hold  . Choose the color you want to fill the circle with. Click the Edit menu in the GIMP menu bar and select "Fill with FG color."