There's an easier way to do this using ironed coffee filters. Sew the pressed flat coffee filter to the right side of your circle fabric with 1/4" seam allowance. Make a small clip in the filter and turn right side out and press. Then you can machine sew the circle to your background fabric, either blind hem or blanket stitch or zigzag. Cut apart into four at the centers. Coffee filters come in quite a few sizes.
Hope this helps. Jenny