Well now that you've been well instructed on how to cut a perfect circle. Maybe I can help you with sewing a perfect circle. :)
There is a "Circular Sewing Attachment" available for at least: Janome, Viking, Brother Innovis (don't know about other brother machines), Singer, Kenmore and I'm not sure who else. You could check with the manufacturer of your machine and see if they have come out with one yet.
Saw one in action on Fons and Porter - but I can't find that right now. Here's a You-Tube video from Brother that demonstrates theirs.
http://www.youtube.com/watch?v=180NDoeRGDU
Good luck!