You will need

- Ruler, compass, pencil.

Instruction

1

Draw a circle, or find the radius of the existing circle. If the circle is not specified, just draw it, setting a comfortable distance between the legs of a compass. Do not change this distance after the tracing of the circle. If you want to split an existing circle, you will have to first determine its radius. To do this, draw a segment that intersects a circle at two points A and B. Using a compass and straightedge, construct the perpendicular bisector to the segment [A; B], divide it into two equal parts. He crosses the circle at points C and D. Construct a perpendicular to the same segment [C; D]. Let it intersect the circle at the points E and F. the intersection of the segments [E; F] and [C; D] be the center of the circle. Put the needle of a compass at any point on the circle and move the other leg so that it was installed in the point of intersection of the segments [E; F] and [C; D]. The radius of the circle found.

2

Divide the circumference into six parts. Install the needle of a compass at any point on the circle. Draw two arcs that intersect the circle at two points. The distance between the legs of the compass should be equal to the radius of the circle. In other words, it has to be that as established in the previous step. Move the leg of a compass with the needle in the intersection of the arcs and one circle. Again watertite two arcs that intersect the circle. Move the compasses to the next point of intersection of the arcs of the circle and create arcs until you find the six points that divide the circumference into six equal parts. Let it be point A, B, C, D, E, F.

3

Construct a regular hexagon inscribed in a circle. For this purpose connect the dots A-B-C-D-E-F-A.

4

Divide the circumference into twelve parts. Construct a perpendicular to the segments [A; B], [B; C], [C; D], dividing them into two equal parts. Let the points of intersection of these normals with the circumference will be A', B', C', D', E', F'. The points A, A', B, C', C, E, D, B', E, D', F divide the circumference into twelve equal parts.

Note

Be careful when working with a compass. If in the process of dividing the circumference into six parts to change the distance between his legs, everything will have to start again.

Useful advice

Use a metal ruler and a firm pencil. So the accuracy of the build will be higher.

# Advice 2: How to divide a circle

The division of a circle into equal parts is usually used to build regular polygons. In principle, it is possible to divide

**a circle**into pieces with a protractor, but sometimes it is inconvenient and inaccurate.Instruction

1

To divide

**a circle**into three equal parts, spread the compass to the radius of the circle. Then set the needle of the compass on one of the axial lines and build the auxiliary**circle**. Three equal parts are indicated by the points of intersection of auxiliary and main circles and a point lying at the opposite end of the centerline.2

To divide

**the circumference**into six parts, then do the same for the other axis. Then get six points on the circle.3

The division of the circle into four parts - trivial task. Four points on the intersection of two perpendicular axial and circumference of a circle will divide

**the circumference**into four equal parts. To divide**a circle**into 8 parts, it is necessary to divide an arc corresponding to 1/4 of the circumference in half. Then breed a pair of compasses to the distance marked in red in the figure, and delay is the distance from the already obtained four points.4

To divide

Repeat all these actions mirror to break up

**a circle**into five equal parts, first divide the radius on centerline in half. At this point install the needle of the compass, and stylus take before crossing perpendicular to this axis and radius of the circle. In the figure this distance is shown in red. Delay is the distance on the circumference, starting from the axis, and then shifting the compass to the resulting intersection.Repeat all these actions mirror to break up

**a circle**into 10 equal parts.