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
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
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
is the Clawson point, is the triangle centroid,
is the incenter,
is the Feuerbach
is the orthocenter, is the de Longchamps point,
is the mittenpunkt,
is the nine-point
is the Nagel point, is the triangle area,
is the inradius.
See alsoBrocard Points
, Cleavance Center
, Taylor Center
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ReferencesCasey, 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,
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."
C. "Encyclopedia of Triangle Centers: X(10)=Spieker Center." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X10.
on Wolfram|AlphaSpieker Center
Cite this as:
Weisstein, Eric W. "Spieker Center." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpiekerCenter.html