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Cut a strip of wood about 1/2" longer than the measurement of the radius of the circle you want to cut. Drill holes through both ends, using a ruler to make sure the holes are spaced at the end points of the radius measurement.
Place a sharp point through one end at the center of the circle to act as a pivot. Put a pencil through the other hole, and pivot the piece of wood 360 degrees to draw a circle. This technique can also be used with a shelving bracket, which already has holes for your pivot point and pencil.
A compass is the traditional tool for drawing precise circles, and its sharp point acts as a pivot. A pencil is attached to the other end. To set the compass to the desired radius, use a ruler to adjust the two end points to the desired length. Place the pivot in the center of the circle and move the pencil 360 degrees to draw the circle.
To make an octagon, start with a piece of wood that's perfectly square. Place the sharp point of a compass on one corner of the square, and adjust it so the pencil tip hits the middle of the square. Lock the compass in position. Use the compass to draw angles from each corner.