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Schiffler Point


SchifflerPoint

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions

alpha_(21)=1/(cosB+cosC)
(1)
alpha_(21)=(b+c-a)/(b+c),
(2)

and is Kimberling center X_(21) (Kimberling 1998, p. 70).


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References

Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Schiffler Point." http://faculty.evansville.edu/ck6/tcenters/recent/schiff.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(21)=Schiffler Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X21.Nguyen, K. L. "On the Complement of the Schiffler Point." Forum Geometricorum 5, 249-254, 2005. http://forumgeom.fau.edu/FG2005volume5/FG200521index.html.Schiffler, K.; Veldkamp, G. R.; and van der Spek, W. A. "Problem 1018 and Solution." Crux Math. 12, 176-179, 1986.

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Schiffler Point

Cite this as:

Weisstein, Eric W. "Schiffler Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchifflerPoint.html

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