You will need

- - the range;
- pencil;
- a pair of compasses.

Instruction

1

Construct a chord of a given circle. Using a ruler, draw a segment so that it crosses

**the circumference**at two points. Let it be point A and B. it is Desirable that these points were located at a sufficient distance from each other.2

Construct a perpendicular bisector intersecting the segment AB and dividing it by the point of intersection into two equal parts. Install between the legs of a compass distance slightly larger than the length of the segment AB, but of obviously greater length of half of this cut. Set the needle of a compass at point A. Watertite

**circumference**. Install the needle of the compass at point B. Watertite another**circle**. Swipe cut through the point of intersection of the circles drawn so that it crossed the segment AB at a single point (let this be point C) and the initial**circle**at two points (let it be D and E).3

Construct a perpendicular bisector that intersects the segment DE and dividing it by the point of intersection into two equal parts by a method similar to that described in the second step. Let built the segment intersects

**the circle**at points F and G, and the segment DE at point O. Point O will be the center of the circle.4

Set the distance between the legs of a compass equal to the radius of the circle. Place the needle of the compass at point D. Place the end of the other leg of the compass at point O.

5

Find the points of two angles of an equilateral

**triangle**inscribed in**a circle**. Without moving leg of a compass with a needle (point D) and the distance between the legs of a compass installed in the previous step, draw**a circle**. This**circle**crosses the original**circle**at two points. Let it be the points H and I.6

Insert an equilateral triangle in

**a circle**. Pairwise line segments connect the points E, H and I. the Triangle with sides EH, HI, and EI is equilateral and is inscribed in the originally given**circle**.