Geometric analysis explores circle properties in triangles, indicating relationships among triangle elements.
In this paper, two types of circles related to a triangle in the Euclidean plane are studied: circles with a center at one vertex that pass through the midpoints of opposite sides, and circles with a center at one vertex that pass through the remaining vertices. The properties of these circles are studied and proved by using barycentric coordinates.
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Volenec et al. (2026) studied this question.
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