How to divide a circle into 7 equal parts

The division of circles into equal parts is very convenient for constructing various regular polygons. The construction can be performed without a protractor, using only a compass and straightedge.

You will need

• Pencil, ruler, pair of compasses, a sheet of paper

Instruction

1. A circle can be divided into 7 equal parts using only a compass and straightedge. To do this, select the point where will be the center of your circle. Mark it as point O.
2. Draw with your compass a circle of the desired diameter with the center at point O.
3. With a ruler and pencil, draw a diameter line passing through the center of the circle. Designate as A and B the two points at which the diameter intersects the circumference.
4. From point A, draw an arc inside the circle. The radius of the arc should be equal to the radius of the circle. The arc must intersect the circle at two points.
5. Mark the points where the arc intersects the circle as C and C1.
6. With a ruler connect the points C and C1 segment.
7. The point at which the segment between points C and C1 intersects the diameter AB of the circle, mark the point D.
8. With the help of a compass put the distance between points C and D on a circle 7 times. To do this, place the tip of a compass at a random location on the circumference, for example at the point A. Mark drawing part one of the compass anywhere on the circle. Place the tip of a compass at the marked point and similarly mark the next point. Mark in this way the whole circumference.
9. Connect with a ruler and pencil all the marked points on the circle with its center at the point O.