# How to build a regular decagon

Challenges for the implementation of the construction of a regular geometric shapes train spatial perception and logic. There are many very simple tasks of this kind. Their decision comes down to modifying or combining already known examples. However, there are those on the solution of which is necessary to think. One of the trivial is the problem of how to construct a regular decagon.

### You will need:

- paper; - Compasses; - Line; - Pencil.

## Instruction how to construct a regular decagon

Step 1:

Draw a circle with a radius of any known center. Indicate on the surface of the point O, which will be the center. Choose the best solution compass legs. Set the needle in the compass point O. Draw the circle.

Step 2:

Draw a line segment passing through the center of the circle and intersects it at two points. With Draw the line segment passing through O point so that it crossed the line twice the circumference. One of the points of intersection draw a line and a circle mark A, the other - P1.

Step 3:

Draw a line segment passing through the point O and perpendicular to the segment OA. Set the compass needle to point A, set the leg of a compass with a pencil at the point P1. Draw the circle. Without changing the legs of the solution, set the compass needle to point P1. Draw the circle. Draw a line segment passing through the intersection point of the circles traced. It will take place also through O. Mark the intersection point of the segment of the circle O as B and P2.

Step 4:

Find a point belonging to the segment OB and equidistant from its ends. To make this action, similar to that described in the third step for constructing perpendiculars to OB, dividing it into two equal parts. Mark found a point C.

Step 5:

Draw the circle with center C and radius CA. Set the compass needle to point C. Place the leg of a compass with a pencil at point A. Draw a circle. Label the point of intersection of this circle with the segment OP2 as a D.

Step 6:

Construct a regular pentagon. Install the foot with a compass needle to point A. Set the leg with a pencil compass to point D. Now the length between the ends of the legs of a compass is the side of a regular pentagon inscribed in a circle with the center notch O.Sdelayte compass on the circle O in the direction of travel in a clockwise direction (the needle compasses is at point a). Designate the resulting point E. Without changing the legs of the solution, move the needle to the point E. Make one more notch. Designate a current F. In doing so, consistently build points G and H. Pairwise connect the points A, E, F, G, H segments. Figure AEFGH is a regular pentagon.

Step 7:

Construct a regular decagon. By segments AE, EF, FG, GH, HA construct perpendiculars, dividing them into two equal parts. Perform steps similar to those that have been described in the third step, to build dividing perpendicular to each otrezku.Stroyte perpendiculars so that they intersect a circle with center O. Let the points of intersection perpendicular to the segments AE, EF, FG, GH, HA O be the circle I, J, K, L, M and sootvetstvenno.Postroyte segments AI, IE, EJ, JF, FK, KG, GL, LH, HM, MA. AEJFKGLHM polygon will be a regular decagon.