You will need

- compass
- - line
- - protractor

Instruction

1

Let there be a circle of radius R. it is Necessary to divide it into three equal parts with a compass. Open the compass to the radius of the circle. You can use this line, but you can put the needle of the compass in the center of the circle, and a leg to take to the circumference describing a circle. The range in any case will be useful later.Install the needle of the compass at an arbitrary position on the circumference describing a circle, and the pen to draw a small arc that intersects the outer contour of the circle. Then set the needle of the compass at the intersection point and again draw a arc with the same radius equal to the radius of the circle). Repeat these steps until the following point of intersection does not coincide with the first. You will receive six points on a circle, placed at equal intervals. It remains to choose three points in one line and connect them with the center of the circle and you will get a circle divided sodium.

2

To divide the circle into three parts with a protractor, just remember that a full rotation around its axis is 360°. Then the angle corresponding to one third of a circle, is 360°/3 = 120°. Now put three times the angle of 120° on the outer side of the circle and connect the resulting points on the circle with centre.

Note

If you connect the dots not with the center, and together, we get an equilateral triangle.

The method described in the first step also allows you to divide the circle into six equal parts.

The method described in the first step also allows you to divide the circle into six equal parts.

# 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.# Advice 3 : How to divide a circle into 5 parts

Certainly, in life, each person had to cut

**a round**cake into pieces. It is easy to do because each segment of the dessert, only approximately equal to his "brother", because he cut "by eye". And how to divide it so that all the parts were exclusively equal to each other? Now that's a mathematical problem, whose solution is reduced to the practical work in geometry: the division of a circle into parts. This requires skills with protractor, compass, straightedge, and pencil. Of course, to measure the angular measure and draw pencil marks on the cake should not be, it is better to practice on paper.You will need

- Protractor, compass, ruler, pencil.

Instruction

1

Let the circle should be divided into five equal parts. You need to perform the following algorithm:

1) Draw on paper with a compass a circle of any diameter. To mark its center (it will be indicated by the needle of a compass). To arbitrarily specify the radius of the circle, connecting two points - the Central and any point on the circle.

1) Draw on paper with a compass a circle of any diameter. To mark its center (it will be indicated by the needle of a compass). To arbitrarily specify the radius of the circle, connecting two points - the Central and any point on the circle.

2

2) due To the fact that the circle in degree measure equal to 360 degrees, it is necessary to divide this angle into five equal parts (360/5=72). So each segment of the circle is equal to 72 degrees. For separation of parts of the figure required a protractor. It should be placed on the circle so that the centers of the circle and the protractor is aligned, and an indication of zero degrees coincides with the radius. Thus, the radius will lie on the line, seinaosa zero degrees and one hundred and eighty degrees on the meter. Then measure on the protractor 72 degrees and build another radius.

3

3) to Build a similar way every 72 degrees three radius, applying a protractor to the last drawn. Make sure that all available five radii located from each other at the same degree and to conclude that the circle is divided into five equal parts.

Useful advice

In the same way you can divide a circle into any number of parts. You need only to divide 360 degrees by the specified number of segments.

# Advice 4 : 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

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 5 : How to divide a circle into 5 parts

The circumference cannot be accurately measured with a ruler, but because of its division into equal parts is a daunting task, especially if these parts an odd number. The division of the circle into five parts is carried out using a conventional compass or a protractor. Divide the circumference into five parts, inscribing in it regular Pentagon.

You will need

- Ruler without graduations, compasses, protractor

Instruction

1

Construct a circle with center at a point Of arbitrary radius. Through the center of the circle are the diameter, name it, for example AV. Construct another diameter of this circle perpendicular to the diameter AB. To do this, swipe from the points A and b two circles with radii larger than the radius of the constructed circle. Through the points in the point of intersection, and through the point guide diameter perpendicular to the diameter AB. Let's call it CD.

With this construction, drawing a circle from points A and O, construct a point E, which is the midpoint of AO. The radius of the COE, from the centre in point E, slide a circle and find the point of intersection with the segment AB. At the intersection of the point F.

With this construction, drawing a circle from points A and O, construct a point E, which is the midpoint of AO. The radius of the COE, from the centre in point E, slide a circle and find the point of intersection with the segment AB. At the intersection of the point F.

2

The resulting cut CF and a side of a Pentagon inscribed in the circle. Compass hold a piece of CF. Let the first point of division, will S. Guide from the radius CF a circle to the intersection of the divisible circle. From the resulting point again swipe the circumference of the same radius as before the new intersection with the circle. Repeat this operation two more times. As a result, the circumference will have five points which are the vertices inscribed in it of a regular Pentagon.

The arc between the points are equal, which means that the circumference divided into five equal parts. You can then divide the circle. To do this, from the point Of swipe segments to the points dividing a circumference. The result is five sectors are the same size, which divide the circle into equal parts.

The arc between the points are equal, which means that the circumference divided into five equal parts. You can then divide the circle. To do this, from the point Of swipe segments to the points dividing a circumference. The result is five sectors are the same size, which divide the circle into equal parts.

3

To divide a circle into five equal parts, use a protractor. Swipe the radius of the circle and from the center and the radius put the angle of 36º. The angle will describe a sector, whose area is equal to 1/5 of the area of the circle. Do this three times, having five equal sections, which will divide the circle into five equal parts.

# Advice 6 : 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.

# Advice 7 : How to divide a circle into five parts

The division of a circle into five equal

**parts**– a fairly simple procedure with the knowledge of some tricky techniques to do it perfectly accurately. This task is very easy to handle, armed with a compass or a protractor.You will need

- a pair of compasses;
- - the range;
- - protractor

Instruction

1

Take a compass and a blank sheet of paper and construct

**a circle**of arbitrary radius with center at point O. Through point O, with a ruler the diameter of the guide, calling it, for example, AV. Then construct another diameter of this circle which is perpendicular to the diameter AB. To do this swipe from dots and 2 circles whose radii will be the radius of the constructed circle. Through their intersection and the point On put the diameter perpendicular to the diameter AB. Name it, for example CD.2

In the same way, conducting

**a circle**of dots A and d, mark the point E, which is the midpoint of AO. CE radius from the center point e of the guide**circumference**. The point of intersection with the segment AB, label as F.3

Cut the CF side of a Pentagon inscribed in the held

**circumference**. Take a compass cut CF. From point C with a radius CF swipe**the circle**to the intersection with**the circumference of**the u - basis. Then from the resulting point again to swipe**a circle**of the same radius before the new intersection with the shared object. Repeat this step two more times. In the end the circle will turn five vertex points of the inscribed Pentagon in it. Between the points of the arc are equal. Point O set aside the segments to the points which divide**the circumference**. You have 5 sectors of equal area, dividing the circle into equal parts.4

To divide

**a circle**into five equal**parts**, you can use a protractor. Swipe the radius of the circle, then its centre and a given radius put an angle of 36°. This angle will describe a sector, an area equal to 1/5 the area of the circle. After performing this operation 3 more times, you will receive 5 equal sections, dividing**the circumference**into five equal**parts**. Thus, there are several ways of solving this problem and choosing any of them you will achieve the exact result.