You will need
- - the range;
- a pair of compasses.
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.
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).
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.
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.
Find the points of two angles of an equilateral triangleinscribed 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.
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.