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Taylor Center


The center of the Taylor circle. It has triangle center function

 alpha_(389)=cosA-cos(2A)cos(B-C)

and is Kimberling center X_(389), which is the center of the Spieker circle of the orthic triangle of the reference triangle (Johnson 1929, p. 277).

The Taylor center lies on the Brocard axis.

TaylorCenter

For an acute triangle DeltaABC, the Taylor center of DeltaABC is the Spieker center of the orthic triangle DeltaH_AH_BH_C.


See also

Altitude, Orthic Triangle, Spieker Center, Taylor Circle

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References

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 277, 1929.Kimberling, C. "Encyclopedia of Triangle Centers: X(389)=Center of the Taylor Circle." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X389.

Referenced on Wolfram|Alpha

Taylor Center

Cite this as:

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

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