Lester's theorem

Lester's theorem states that a triangle’s circumcenter, two isodynamic centers, and two Fermat points lie on one circle, called the Lester circle.

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Circumcenter: The point equidistant from a triangle’s three vertices, serving as the center of its circumscribed circle. It is one of the five centers on the Lester circle.
Lester circle: The circle passing through a triangle’s circumcenter, two isodynamic centers, and two Fermat points. It is the common circle whose existence Lester’s theorem asserts.
Triangle geometry: The study of properties and relationships among triangles and their associated points, lines, and circles. Lester’s theorem is a notable concyclicity result within this subject.
Equilateral triangle: A triangle whose three sides and three angles are equal. Its symmetry makes the triangle centers coincide in ways that degenerate the usual Lester-circle configuration.
Isodynamic point: A triangle center where the three distances to the vertices are proportional to the opposite side lengths. Both isodynamic points of the triangle lie on the Lester circle.
Barycentric coordinates: A coordinate system that represents points in a triangle’s plane using weights assigned to its vertices. Triangle centers can be expressed in barycentric coordinates to verify the collinearity and concyclicity relations involved.
Dynamic geometry software: Software that constructs geometric objects and lets them be manipulated while preserving specified relationships. Dragging triangle vertices can illustrate that the five centers remain concyclic.
Scalene triangle: A triangle with three sides of different lengths. A generic scalene triangle displays the distinct centers in Lester’s concyclicity claim.
Fermat point: A triangle center minimizing the sum of distances to its three vertices, with angles of 120 degrees when all angles are below 120 degrees. The first and second Fermat points supply two more points on the circle.
Concyclic points: Points that all lie on one circle. The theorem’s central geometric claim is that its five centers are concyclic.