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Jerabek Center

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JerabekCenter

The Jerabek center is the center of the Jerabek hyperbola. It is Kimberling center X_(125), which has equivalent triangle center functions

alpha_(125)=cosAsin^2(B-C)
(1)
alpha_(125)=((ccosC-bcosB)^2)/(cosA)
(2)
alpha_(125)=bc(b^2+c^2-a^2)(b^2-c^2)
(3)

(Kimberling 1998, p. 87).

See also

Jerabek Antipode, Jerabek Hyperbola

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References

Bui, Q. T. "Pedals on Circumradii and the Jerabek Center." Forum Geom. 6, 205-212, 2006.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(125)=Center of Jerabek Hyperbola." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X125.

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Jerabek Center

Cite this as:

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

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