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# Spieker Center

The Spieker center is the center of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle . It is also the center of the excircles radical circle.

It has equivalent triangle center functions

 (1) (2)

and is Kimberling center .

The Spieker center is also the centroid of the perimeter of the original triangle, as well as the cleavance center (Honsberger 1995; illustrated above).

The Spieker center lies on the Nagel line, and is therefore collinear with the incenter, triangle centroid, and Nagel point.

It lies on the Kiepert hyperbola.

The Spieker center, third Brocard point, and isotomic conjugate of the incenter are also collinear.

Distances to other named triangle centers include

 SpCl (3) (4) (5) (6) (7) (8) (9) SpNa (10)

where is the Clawson point, is the triangle centroid, is the incenter, is the Feuerbach point, is the orthocenter, is the de Longchamps point, is the mittenpunkt, is the nine-point center, is the Nagel point, is the triangle area, and is the inradius.

Brocard Points, Cleavance Center, Cleaver, Incenter, Isotomic Conjugate, Nagel Line, Perimeter, Spieker Circle, Taylor Center, Triangle Centroid

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## References

Casey, J. A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., p. 81, 1893.Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 3-4, 1995.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 226-229 and 249, 1929.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Spieker Center." http://faculty.evansville.edu/ck6/tcenters/class/spieker.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(10)=Spieker Center." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X10.

Spieker Center

## Cite this as:

Weisstein, Eric W. "Spieker Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpiekerCenter.html