How to divide a circle into 12 parts

The geometric construction is an important part of the training program. They develop imagination, logic and spatial thinking. Most of the tasks on the build should be solved only with the help of ruler, compass and pencil. This allows you to consolidate the perception of dependencies between parameters of geometric objects. Some of them are simple and natural, and some are not visible clearly. So, to build the diagonal of a square or an isosceles triangle is not difficult, and over how to divide the circle into 12 parts, have to think a little.

You will need

Ruler, compass, pencil.

Instruction

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.

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.

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

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.

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