Трапеція, збагачена колом: геометричні властивості та теореми

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.