Tasks on geometrical constructions very well develop spatial and logical thinking and therefore are one of the main parts of the school curriculum. As well as in any subject domain, there are standard and non-standard tasks. It is possible to refer to standard tasks, for example, creation of an equilateral triangle. In the course of construction the triangle is inscribed in a circle. But how to be if it is necessary to enter an equilateral triangle in a circle which is already constructed?
It is required to you
- - ruler;
- - pencil;
- - compasses.
Instruction
1. Construct a chord of the set circle. By means of a ruler draw a piece so that it crossed a circle in two points. Let it will be points of A and B. It is desirable that these points were located on sufficient removal from each other.
2. Construct the perpendicular crossing a piece of AB and dividing its point of intersection into two equal parts. Establish between compasses legs distance, a little smaller AB piece lengths, but obviously bigger lengths of a half of this piece. Establish a compasses needle in A point. Draw a circle. Establish a compasses needle in B point. Draw one more circle. Carry out a piece through points of intersection of the drawn circles so that it crossed AB piece in one point (let it will be a point of C) and an initial circle in two points (let it will be points of D and E).
3. Construct the perpendicular crossing a piece of DE and dividing its point of intersection into two equal parts in the way similar to described in the second step. Let the constructed piece cross a circle in points of F and G, and DE piece in O point. The point of O will be the center of a circle.
4. Establish distance between compasses legs equal to circle radius. Place a compasses needle in a point of D. Place the end of other leg of compasses in O point.
5. Find points of two corners of an equilateral triangle, inscribed in a circle. Without changing position of a leg of compasses with a needle (in a point of D) and the distances between compasses legs established on the previous step, draw a circle. This circle will cross an initial circle in two points. Let it will be points of H and I.
6. Enter an equilateral triangle in a circle. In pairs connect pieces of a point of E, H and I. The triangle with the parties of EH, HI and EI will be equilateral and entered in the circle set initially.