Lester's theorem

In Euclidean plane geometry, Lester's theorem, named after June Lester, states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle.

Lester's circle theorem follows from a more general result by B. Gibert (2000); namely, that every circle whose diameter is a chord of the Kiepert hyperbola of the triangle and is perpendicular to its Euler line passes through the Fermat points.

In 2014, Dao Thanh Oai showed that Gibert's result follows from a property of rectangular hyperbolas. Namely, let ${\displaystyle H}$ and ${\displaystyle G}$ lie on one branch of a rectangular hyperbola ${\displaystyle S}$, and ${\displaystyle F_{+}}$ and ${\displaystyle F_{-}}$ be the two points on ${\displaystyle S}$, symmetrical about its center (antipodal points), where the tangents at ${\displaystyle S}$ are parallel to the line ${\displaystyle HG}$,

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