Such polygon which all parties concern the circle entered in it is called described. It is possible to describe only a regular polygon, that is such at which all parties are equal. Still ancient architects when it was necessary to design, for example, a column faced the solution of a similar task. Modern technologies allow to make it with the minimum time expenditure, however the principle of work remains to the same, as in classical geometry.
It is required to you
- - compasses;
- - protractor;
- - ruler;
- - sheet of paper.
Instruction
1. Draw a circle with the set radius. It define the center as About and carry out one of radiuses that there was an opportunity to begin construction. To describe around it a polygon, you need to know its only parameter — the number of the parties. Designate it as n.
2. Remember, what it is equal to central a corner of any circle. It makes 360 °. Proceeding from it, it is possible to calculate corners of sectors which parties will connect the center of a circle to points of contact it with the parties of a polygon. The number of these sectors equals to number of the parties of a polygon, that is n. α find a sector corner on a formula α = 360 ° / n.
3. By means of a protractor postpone the received corner size from radius and carry out through it one more radius. That calculations were exact, use the calculator and round sizes only in exceptional cases. From this new radius postpone a corner of the sector again and draw one more straight line between the center and the line of a circle. In the same way construct all corners.
4. Choose one of radiuses. In a point of its crossing with a circle carry out a perpendicular to both parties. You do not know the size of the party of a polygon yet therefore make lines longer. Carry out just the same perpendicular to the following radius before its crossing with the first. Designate the received top as A. Nachertite a perpendicular to the third radius and with the second designate a point of its crossing as Century. Thus carry out perpendiculars and to all other radiuses. Designate tops by letters of the Latin alphabet. Clean excess lines.
5. At you the polygon with the number of the parties, equal n turned out. It is divided into isosceles by triangles the lines drawn from the center of the circle entered in it to corners. As a polygon are correct, triangles turned out isosceles, at each of which height equal to circle radius is known to you. You know and a corner of the sector which is divided by this height into 2. Proceeding from the obtained data, calculate length of a half of the party according to the theorem of sine or tangents.