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This article presents a series of math problems of elevated complexity, primarily solvable through geometric reasoning. These problems revolve around a geometric configuration of a triangle with an arbitrary point inside it. Each problem is accompanied by an original solution, with solution methods progressing from simple to intricate. Intended for mathematics educators, the article serves as a resource for use in upper-level classes and supplementary sessions for advanced geometry studies. The content provided herein is also beneficial for mathematics university students and individuals seeking to independently deepen their knowledge of geometry.
Liudmyla Hetmanenko (Mon,) studied this question.