Schiffler Point
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High Quality Content by WIKIPEDIA articles! In geometry, the Schiffler point of a triangle is a point defined from the triangle that is invariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985). 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. Trilinear coordinates for the Schiffler point are left[frac{1}{cos B + cos C}, frac{1}{cos C + cos A}, frac{1}{cos A + cos B}right] or, equivalently, left[frac{b+c-a}{b+c}, frac{c...
High Quality Content by WIKIPEDIA articles! In geometry, the Schiffler point of a triangle is a point defined from the triangle that is invariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985). 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. Trilinear coordinates for the Schiffler point are left[frac{1}{cos B + cos C}, frac{1}{cos C + cos A}, frac{1}{cos A + cos B}right] or, equivalently, left[frac{b+c-a}{b+c}, frac{c+a-b}{c+a}, frac{a+b-c}{a+b}right] where a, b, and c denote the side lengths of triangle ABC.
