The following set of videos show how to cut circles using a router in a piece of wood. They show how to create a template to create different diameter circles.
How to Build a Circle Cutting Jig for Your Router by blazingnailgun –
How to make a large circle jig quick & easy | Router Tips by Alex Knappenberger-
This last video shows you how to cut perfect circles if you have a router bench.
Woodworking-“Cutting Perfect Circles” Action Video by izzy swan