# How to divide the circle into 12 parts

Geometric constructions - an important part of the training program. They develop imagination, logic and spatial thinking. Most of the construction problems should be solved solely with a ruler, a compass and a pencil. This makes it possible to consolidate the perception of dependency between the parameters of geometric objects. Some of them are simple and natural, and some are not clearly visible. So, to build a diagonal of a square, or an isosceles triangle is not difficult, but over how to divide a circle into 12 parts, it is necessary to think a little.

### You will need:

The ruler, compass and pencil.

## Instruction how to divide a circle into 12 parts

Step 1:

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

Step 2:

Divide the circle into six parts. Set the compass needle at any point of the circle. Draw two arcs that intersect the circle at two points. The distance between the legs of the compass must be equal to the radius of the circle. In other words, it must be such as has been found in the previous step. Move the leg of a compass with the needle in the point of intersection of a circle and arcs. Again Draw the two arcs that intersect the circle. Move the leg of a compass in the next point of intersection of the arcs of the circle arc and build until you find the six points that divide the circle into six equal parts. Let it be point A, B, C, D, E, F.

Step 3:

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

Step 4:

Divide the circle into twelve parts. Draw perpendiculars to the segments [A; B], [B; C], [C; D], dividing them into two equal parts. Let the data points of intersection of the perpendiculars with the circle are A ', B', C ', D', E ', F'. Points A, A ', B, C', C, E ', D, B', E, D ', F divide the circle into twelve equal parts.