On some unknown results related to the nontrivial properties of ordinary triangles. part 1

In this paper, it was given a detailed solution of many original problems, formulated by Fedorov B. P. some time ago. These problems belong to the various nontrivial properties of Euclidean triangles. When presenting the material, it has been used some universally accepted, but not very popular in modern textbooks on geometry terminology, which is nesessary for understanding and in-depth perception of the problems described in the paper.