According to definition if all tops of a polygon belong to a circle, it is called "entered". It is simple to construct on paper such figure, especially if all parties making it have identical length. For the correct triangle such construction can be executed in several ways, and the choice of the most convenient depends on the available tools.
It is required to you
- Paper, pencil, compasses, ruler, calculator, protractor.
Instruction
1. If you have an opportunity to use a protractor at construction, begin with the choice of any point on a circle which has to become one of tops of the correct triangle. Designate it, for example, by letter A.
2. Draw an auxiliary piece, having connected a point And to the center of a circle. Apply a protractor to this piece so that zero division coincided with the center of a circle, and put the auxiliary end at mark 120 °. Through this point carry out one more auxiliary piece from the beginning in the center of a circle and the termination on crossing with a circle. Designate a point of intersection by letter B - it is the second top of the entered triangle.
3. Repeat the previous step, but put a protractor to the second auxiliary piece, and designate a point of intersection with a circle by letter C. More protractor is not required.
4. Connect points And yes In, In and With, With and And. On it creation of the correct triangle inscribed in a circle will be complete.
5. If there is no protractor, but there are compasses and the calculator, then begin with calculation of length of the party of a triangle. You for certain know that it can be expressed through the radius of a circumscribed circle, having increased it by the relation of the three to a square root from the three, that is approximately on 1.732050807568877. Round this number to the necessary degree of accuracy and increase by circle radius.
6. Note any point on a circle and designate it by letter A - it is the first top of the correct triangle.
7. Postpone length of the party of a triangle found on the fifth step on compasses and draw an auxiliary circle with the center in a point And. Designate points of intersection of two circles by letters B and C - it is two other tops of the correct triangle entered in a circle.
8. Connect points And yes In, In and With, With and And yes construction will be complete.