AUXILIARY CIRCLE METHOD IN PLANIMETRIC PROBLEMS OF THE UNIFIED STATE EXAM

Abstract

One of the most important educational goals of modern school is to prepare students for the successful completion of final exams. The structure of the Unified Sate Exam in profile-level mathematics includes the proof of increased complexity for geometric problems, requiring students to have a comprehensive knowledge of planimetry. The most important feature is the lack of unified algorithms for solving such problems; the success largely depends on the students’ experience in solving combined planimetric problems. Nevertheless, the practice of solution allowed us to identify some geometric structures that are auxiliary keys to finding the right solution. One of these keys was the auxiliary circle method, which is presented in this paper. The paper describes the essence of the method and the conditions of its application, examines the proofs for the problems taken from real test and measurement materials of the exam, and considers the solutions of the problems in the framework of the described method.