Triangle of three centers of exscribed circles

Гетманенко, Людмила Миколаївна (2024) Triangle of three centers of exscribed circles Grail of Science (46). pp. 716-721. ISSN 2710–3056

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Abstract

The paper investigates the properties of the triangle formed by the centers of the three excircles, γ_a, γ_b, γ_c, constructed for an arbitrary triangle ABC. Geometric relationships between the triangle ABC and the triangle I_a, I_b, I_c are examined, along with the properties arising from this construction. It is shown that the triangle ABC is orthocentric to the triangle I_a, I_b, I_c, and the circumcircle of triangle ABC simultaneously serves as the Euler circle of triangle I_a, I_b, I_c. New formulas for the sides of triangle I_a, I_b, I_c are proposed, as well as positional problems for constructing triangle ABC given specific points. The connection between the elements of these triangles and the Euler circle is revealed for the first time, and previously unpublished problems are introduced for solution.

Item Type:	Article
Uncontrolled Keywords:	excircle; Euler circle; nine-point circle; orthocentric triangle; positional problems; semicircle on a triangle’s side as a diameter
Subjects:	Статті у базах даних > Index Copernicus
Divisions:	Інститут післядипломної освіти > Кафедра природничо-математичної освіти і технологій
Depositing User:	Людмила Гетманенко
Date Deposited:	23 Dec 2024 10:15
Last Modified:	08 Jan 2025 09:06
URI:	https://elibrary.kubg.edu.ua/id/eprint/50799

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