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

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

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 .

See also 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 . Referenced
on Wolfram|Alpha Spieker Center
Cite this as:
Weisstein, Eric W. "Spieker Center." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/SpiekerCenter.html

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