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Solving geometry problems is both difficult and interesting. Difficult because there is no general algorithm to solve more or less non-trivial problems as every single problem requires individual and creative approach. At the same time, this is a very interesting activity, because for almost every problem there are plenty of ways to solve it. In this work, we present the method of auxiliary circle divided into equal parts. This method allows finding solution algorithm for some geometry problems which are hard to solve by the method of additional constructions. [ABSTRACT FROM AUTHOR]

The article discusses problems with ambiguous conditions, the solution of which leads to several variants of answer. Such problems are called variative problem. The role of variative problems in intellectual development of schoolchildren in mathematics classes are described in this article. Proposed a methodology for including variative problems in the process of teaching mathematics. [ABSTRACT FROM AUTHOR]

Areas are actively used in the solution of many geometrical problems. In this work, smart and laconic solutions are found for various problems by means of the area method. The well-known trigonometric addition formula is also proved. In the area method, the given formulas are divided into the parts, whose areas are then calculated using problem data. [ABSTRACT FROM AUTHOR]

We consider some applications of Ptolemy's theorem. In particular, we find a criterion for constructing an inscribed hexagon. [ABSTRACT FROM AUTHOR]

This work is dedicated to the study of existence in small of classical solution of multidimensional mixed problem for one class of third order semilinear psevdohyperbolic equations. Conception of classical solution for mixed problem under consideration is introduced. After applying Fourier method, the solution of original problem is reduced to the solution of some countable system of nonlinear inteqro-differential equations in unknown Fourier coefficients of the sought solution. Besides, existence theorem in small of classical solution of the mixed problem is proved by contracted mappings principle. [ABSTRACT FROM AUTHOR]

This work is dedicated to the study of existence and uniqueness of almost everywhere solution of a multidimensional mixed problem for one class of third order differential equations with nonlinear operator on the right-hand side. The conception of almost everywhere solution for the mixed problem under consideration is introduced. After applying the Fourier method, the solution of the original problem is reduced to the solution of some countable system of nonlinear integro-differential equations in unknown Fourier coefficients of the sought solution. Besides, existence and uniqueness theorems of almost everywhere solution of the mixed problem under consideration are also proved in this work. [ABSTRACT FROM AUTHOR]