If each party of a quadrangle concerns a circle only in one point and any of these points does not lie in polygon top, it is possible to call such circle entered. Not it is possible to enter a circle in any quadrangle, but if it is possible, for performance of construction it is required steps.
It is required to you
- Paper, pencil, ruler, compasses, protractor, square.
Instruction
1. Begin with definition of a basic opportunity to carry out the set construction. It is possible to enter in a quadrangle a circle only if the sums of lengths of its opposite sides coincide - measure these pieces, in pairs put and check whether the condition is satisfied.
2. For the most difficult case - creation of the circle entered in a quadrangle of irregular shape - it is necessary to construct bisectors of the corners lying in figure tops. Begin with any top - apply a protractor, measure corner size, divide the received result in half and put the auxiliary end. Draw the auxiliary piece lying on a bisector of this top - it has to begin in top, pass through an auxiliary point and come to an end on the opposite side of a figure.
3. Repeat operation of the previous step for the second top of a quadrangle, and to the place of crossing of two auxiliary pieces put the end. Designate it, for example, letter O - it is the center of an inscribed circle. If from the first step or from statements of the problem unambiguously follows that it is possible to enter a circle in this quadrangle, to build bisectors of corners in two remained tops there is no need. And if check from the first step cannot be made for some reason or other, you should make sure that all four bisectors are crossed in one point. If this condition is not satisfied after repetition of the first step for other tops, means it is impossible to enter a circle in such quadrangle.
4. Determine the radius of an inscribed circle. For this purpose by means of the square or a protractor construct the perpendicular lowered from the center of a circle - a point About - to any of the parties. Postpone length of the turned-out piece on compasses.
5. Draw a circle with a radius postponed on compasses and the center in a point of the Lake. On it construction will be complete.