My favorite way of sewing a circle (like the center of a Dresden Plate) is to draw a circle on fusible web (on non fusible side), place fusible side next to pretty side of fabric, stitch with a short stitch length on drawn circle line, use pinking shears to trim 1/8" around stitching, cut a small slit in the fusible, turn right side out. Now place fusible side down on background fabric with pretty side of circle fabric facing up. Using hot iron, heat set the circle to background fabric, then I like using the blanket stitch and sew around the circle. (all machine stitching)