When I do circles I piece them in. Using a marking pen,I draw a circle on the backing AND on my material the same size. I cut out the top material piece 1/4" bigger. I score the line and press it into the finished circle. On the backing. I cut it out a 1/4"smaller. Using glue stick. I tack the pressed circle over the "hole" using the line as a guide. Then I flip it to the back side and stitch on the pressed line. Try it! Perfect set in circles.
These are the only pictures I have to illustrate this. The first is the material that becomes the circle and the second photo shows the perfect circle sewn in. The circle is about 4 " dia.