Circle-enhanced trapezoid: geometric properties and theorems

Гетманенко, Людмила Миколаївна (2025) Circle-enhanced trapezoid: geometric properties and theorems Grail of Science (52). pp. 725-731. ISSN 2710-3056

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Abstract

This paper explores the geometric properties that arise from the interaction between a trapezoid and a circle. Through a series of specific problems, it is demonstrated how incorporating a circle into the construction of a trapezoid gives rise to new, non-obvious statements that warrant independent theoretical investigation. In analogy with well-known results in triangle geometry—such as Simson’s theorem, Euler’s formula, and the nine-point circle—the combination of a trapezoid and a circle also reveals potential for the discovery of new theorems. The author examines a number of original geometric phenomena related to incircles and circumcircles of trapezoids, and provides proofs of their validity. The work aims to broaden the understanding of the circle as a tool for enriching geometric figures, particularly quadrilaterals.

Item Type:	Article
Additional Information:	https://doi.org/10.36074/grail-of-science.23.05.2025.104
Uncontrolled Keywords:	circle, circumcircle of a trapezoid; incircle of a trapezoid; triangle’s excircle; right trapezoid; inscribed angles; central angles
Subjects:	Статті у періодичних виданнях > Фахові (входять до переліку фахових, затверджений МОН)
Divisions:	Інститут післядипломної освіти > Кафедра природничо-математичної освіти і технологій
Depositing User:	Людмила Гетманенко
Date Deposited:	24 Jun 2025 10:50
Last Modified:	24 Jun 2025 10:50
URI:	https://elibrary.kubg.edu.ua/id/eprint/52186

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