The pentagon is a geometrical figure with five corners and five parties. In geometry the correct pentagon (Pentagon) which corners and the parties are equal is of the greatest interest. It can both be entered in a circle, and to describe around it. It is very important to be able to carry out similar constructions without application of a protractor, usual make-shifts. Thanks to the known properties of a circle and correct pentagon it is possible to enter the Pentagon in a circle only by means of one compasses.
It is required to you
- Compasses, pencil, sheet of paper
Instruction
1. Take the sheet of paper and put in the middle its end of O. Eto there will be a center of a circle. Establish distance of legs of compasses equal to circle radius. Carry out a circle from center O with the set radius.
2. To any place of an arch of a circle put M. Eto's end there will be the first top of the entered pentagon. Through points of M and About carry out diameter of a circle of MN. For creation of a straight line use any improvised subject with the flat party.
3. Construct one more diameter perpendicular to diameter of MN. For this purpose carry out by compasses arches from points of M and N with an identical radius. Radius choose such that both arches were crossed among themselves and with this circle in one point. It will be the first point And the second dimeter. Carry out through it and a point About a straight line. Diameter AV perpendicular to direct MN will turn out.
4. Find the middle of radius IN. For this purpose with a radius of a circle carry out by compasses an arch from a point In so that it crossed a circle in two points With and River. Through these points draw a straight line. This straight line will divide radius IN exactly in half. Put the end To to the place of crossing of CP and BO.
5. Connect points of M and To a piece. Set on compasses distance equal to MK piece. From a point of M carry out an arch so that it crossed the radius of the joint-stock company. To the place of this crossing put the end E. The received distance of ME corresponds to length of one party of the entered pentagon.
6. Construct the remained pentagon tops. For this purpose establish distance of legs of compasses equal to ME piece. From the first top of the Pentagon of M carry out an arch before crossing with a circle. The point of intersection will also be the second top of F. From the received point in turn also carry out an arch of the same radius with crossing of a circle. Receive the third top of the Pentagon of G. The same way construct other points of S and L.
7. Connect the received tops direct pieces. The inscribed in a circle, correct pentagon of MFGSL is constructed.