How to enter a trapeze in a circle

How to enter a trapeze in a circle

Trapeze call a flat quadrangular figure which two parties (bases) are parallel, and two other (sides) have to be not parallel. If all four tops of a trapeze lie on one circle, this quadrangle is called entered in it. It is simple to construct such figure.

It is required to you

  • Paper, pencil, square, compasses.


1. If there are no additional requirements to the entered trapeze, you can use the parties of any length. Therefore begin construction with any point, for example, in the lower left quarter of a circle. Designate it by letter A - there will be one of tops of an inscribed in a circle trapeze.

2. Draw the horizontal line which is beginning in a point And yes coming to an end in the place of crossing with a circle in the lower right quarter of a circle. Crossing designate this place by letter B. The constructed piece of AV is the lower basis of a trapeze.

3. In any convenient way draw the piece parallel to the lower basis located above the center of a circle. For example, if at your disposal there is a square, it can be done so: at first apply it to the basis of AV and draw the auxiliary perpendicular line. Then apply the tool to the auxiliary line above the center of a circle and draw perpendiculars in both parties from it, finishing everyone on crossing with a circle. These two perpendiculars have to lie on one straight line and then they form the top basis of a trapeze. Designate the left extreme point of this basis by letter D, and right - letter C.

4. If there is no square, but there are compasses, then creation of the top basis will be even simpler. Put any point on the left top quarter of a circle. The only condition - she should not settle down strictly vertically over a point And, otherwise the constructed figure will be a square. Designate a point by letter D and lay off on compasses distance between points of A and D. Then establish compasses in a point In and in the right top quarter of a circle note the point corresponding to the laid-off distance. Designate it by letter C and draw the top basis, having connected points of D and Page.

5. Draw sides of the entered trapeze, having carried out pieces of AD and BC.

Author: «MirrorInfo» Dream Team