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.
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.
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.