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In geometry, the Schiffler point of a triangle is a triangle center, a point defined from the triangle that is equivariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985).
Contents
Definition
A triangle ABC with the incenter I has its Schiffler point at the point of concurrence of the Euler lines of the four triangles BCI, CAI, ABI, and ABC. Schiffler's theorem states that these four lines all meet at a single point.
Coordinates
Trilinear coordinates for the Schiffler point are
or, equivalently,
where a, b, and c denote the side lengths of triangle ABC.
References
Schiffler point Wikipedia(Text) CC BY-SA