How to inscribe a regular octagon in a given circle

For constructions in geometry.

Draw the circle. Put in a diameter. construct the perpendicular bisector of this diameter, extended to the circle. Bisect the right angles. extend these angle bisectors to the circle. join the points on the circle.

1. Find the center of the circle. This may be a "given" point, but if not, take 3 arbitrary points on the circle A, B, and C. The center is where the perpendicular bisector of AB meets the perpendicular bisector of BC. (Remember the perpendicular bisector of a chord is a diameter).

2. Once you find the center O, take an arbitrary point D and draw the line OD and note its intersection E with the circle. DE is a diameter of the circle.

3. Construct FG another diameter which is the perpendicular bisector of DE. You now have a square DFEG.

4. Bisect the angles