The first two sets of instructions are for drawing a disc, rather than a circle (a disc being a filled-in circle) and don't extend to drawing a circle easily. The last method does, but it is about 10x as long. The traditional method for drawing a circle was to select the inner circle, save the selection to a channel, grow the selection by the pixel width of the stroke you want, subtract the saved selection, then fill. Wonderful /s
GIMP does not (unless I missed it in a ~recent update) have a shape tool like most image editors. The GIMP documentation in any case suggests using Inkscape for the purpose.