Representatives of various professions constantly face creation of the entered and described polygons. Usually any problems do not cause triangles as it is possible to enter in a circle any figure of this type. With quadrangles the situation is a little differently. At first it is necessary to decide whether it is possible to enter it in a circle in general.
It is required to you
- - a quadrangle with the set parameters;
- - compasses;
- - ruler;
- - protractor;
- - calculator;
- - sheet of paper.
Instruction
1. Measure all corners of the quadrangle given you. Find the sums of opposite corners. It is possible to enter a quadrangle in a circle only if the sums of opposite corners are equal 180 °. Thus, it is possible to construct a circumscribed circle always around a square, a rectangle and an isosceles trapeze.
2. Draw a circle with R radius. Define its center. As a rule, it is designated by letter O. Find any point on the circle and call it any letter. Let's say it will be a point And. Your further actions depend on what quadrangle is given you. At a square of diagonal are perpendicular each other and are radiuses of a circumscribed circle. Therefore construct two diameters between which corner makes 90 °. Consistently connect points of their crossing to a circle straight lines.
3. To enter a rectangle, you need to know a corner between diagonals or the sizes of the parties. In the second case the corner can be calculated, having used Pythagorean theorems, sine or cosines. Carry out one of diameters. Designate it, for example, by points And yes Page. From a point Oh, which at the same time is also the middle of diagonal postpone a corner between diagonals. Through the center and a new point carry out the second diameter. Just as in a case with a square, connect consistently points of intersection of diameters to a circle.
4. For creation of an isosceles trapeze find any point on a circle. Construct from it the chord equal to the top or lower basis. Find its middle and carry out through it and the center of a circle diameter perpendicular to a chord. Postpone the trapeze height size on diameter. Through this point carry out a perpendicular to both parties before crossing with a circle. Connect in pairs the ends of the bases.