Authors: Temur Z. Kalanov
Comments: 22 Pages.
Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
In  we introduced the mixt-linear circles adjointly inscribed associated to a triangle,
with emphasizes on some of their properties. Also, we’ve mentioned about mixt-linear circles
adjointly ex-inscribed associated to a triangle.
In this article we’ll show several basic properties of the mixt-linear circles adjointly exinscribed
associate to a triangle.