A Schiffler Point? That is cool!… Any relationships to persons of the same name (like myself) are purely coincidental.

The Schiffler Point is named for Kurt Schiffler (1896-1986), who introduced the point in a problem proposal:

Kurt Schiffler, G. R. Veldkamp, and W. A. van der Spek, Problem 1018 and Solution, Crux Mathematicorum 12 (1986) 176-179.

An accomplished amateur geometer, Schiffler discovered one of the most attractive of the “twentieth-century” triangle centers, now known as the Schiffler Point. Let I denote the incenter of a triangle ABC. The Schiffler point of ABC is the point of concurrence of the Euler lines of the four triangles BCI, CAI, ABI, ABC. Trilinear coordinates for the Schiffler point are

1/(cos(B) + cos(C)) :
1/(cos(C) + cos(A)) :
1/(cos(A) + cos(B)),

or, equivalently,

(b + c – a)/(b + c) :
(c + a – b)/(c + a) :
(a + b – c)/(a + b),

where a, b, c denote the sidelengths of triangle ABC.

The Schiffler Point
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