The bisector triangle with a 90° angle

Гетманенко, Людмила Миколаївна (2024) The bisector triangle with a 90° angle Grail of Science (35). pp. 232-236. ISSN 979-8-88955-764-7

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Abstract

For the examination of the triangle discussed in the article, profound knowledge of plane geometry is required, and grasping the specific approach to solving it can be quite challenging without prior knowledge of what to rely on. The focus is on a triangle with a 120° angle, commonly known as the Shebarshin problem. The article presents both computational and purely geometric methods for solving a problem of elevated complexity. This particular problem appears in entrance exams for universities and in mathematical Olympiads at the highest levels. The theme of singular triangles remains constantly relevant in geometry. For instance, many properties and theorems are known about an orthocentric triangle, which have been discussed in detail and already proven. I propose to consider in detail the properties and theorems of an equally interesting triangle, the sides of which connect the bases of the bisectors of the interior angles of the triangle. The goal of my article is to alleviate the drawback of complexity while retaining accessibility and originality in the geometric problem involving a triangle with a 120° angle and an inscribed bisectral triangle with a corresponding 90° angle.

Item Type:	Article
Uncontrolled Keywords:	Shebarchin's problem; bisector triangle; triangle bisector property; external bisector of a triangle; interior angle bisector of a triangle; Gauss line
Subjects:	Статті у базах даних > Index Copernicus
Divisions:	Інститут післядипломної освіти > Кафедра природничо-математичної освіти і технологій
Depositing User:	Людмила Гетманенко
Date Deposited:	09 Sep 2024 07:13
Last Modified:	09 Sep 2024 07:13
URI:	https://elibrary.kubg.edu.ua/id/eprint/49651

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