Cutting with a router is the best way to get perfect circles. Its easy if you build a jig that fits on top of your router table. By using a revolving axis that your router follows, your circle will come out perfectly. You can set up the table, make the jig out of ordinary plywood and use it over and over again. You can make it adjustable to cut circles ranging from a few inches to about 32 inches or even bigger.
Remove the router from its mounted position underneath the router table if there is one attached. Set it aside. If your router table has a fence, remove it too.
Screw the 36-by-36-by-3/4 inch plywood to the top of the router table using the cordless drill and 4 screws, 1-1/4 inches.
Drill a 3/8-inch hole in the exact centre of the 36-by-36-inch plywood. Insert the dowel into the hole leaving 2 inches exposed.
Center and drill a hole 4 inches from the end of the 24-by-10-inch plywood using the 3/4 inch bit and cordless drill.
Insert the 1/2-inch cutter bit into the plunge router using the wrenches that came with the router. Adjust the router depth of cut so that the bit extends past the base of the router 1 1/2 inches.
Insert the router bit into the 3/4-inch hole in the 24-by-10-inch plywood, setting the base down on the plywood. Screw the router to the plywood using 3/4-inch screws through the router's base using holes already in the router base for that purpose. The bit should be extending out the bottom of the hole 3/4-inch.
Drill a 3/8-inch hole in the centre of the poplar blank. Position the poplar blank over the dowel. Allow the blank to drop onto the dowel as the dowel penetrates the hole in the blank.
Draw or trace your circle diameter out on the poplar blank using a large compass. Position the router's bit directly on the line of your circle. Swing the plywood attached to the router over the end of the dowel. Mark the point with a pencil where the dowel touches the plywood. Drill the plywood on the mark with the 3/8-inch bit and drop the plywood attached to the router onto the dowel. The router should now move in a circle as it and the plywood strip rotate around the dowel.
Plug in the router. Turn it on and gently push down on the router to a cutting depth of approximately 1/4 inch. Rotate the router around the circle as it cuts. When you come to the point where you started, push down on the router another 1/4 inch and rotate around the circle. When you come to the point you started, push the bit all the way down. Rotate around the circle until the circle is completely cut through.
Don't try to cut through a circle in one pass, its too much for the router to handle. Always make multiple passes.
Always wear safety glasses when working with wood.