Задачи на построение, неразрешимые циркулем и линейкой, и их решение в компьютерной среде

Modeling operations with a compass and a straight-edge on arbitrary real numbers leads to the generalization of a well-known algebraic solving method in constructive geometry. The article presents a new class of tasks which can be almost totally solved with a compass and a straight-edge. On the one hand, this class includes all the tasks which are solved with a compass and a straight-edge, on the other hand, it includes many tasks which are not solved with these tools (in particular, classical tasks of ancient times, tasks on constructing a isosceles triangle on on a bisectrixes etc.). The authors show how they are solved by means of graphic and animation possibilities of the computer environment GeoGebra. The proposed method of computer support in constructive geometry is important not only for specific tasks on constructing, but also in teaching geometry, both in schools and colleges.