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Third Brocard Point


The third Brocard point has triangle center function

 alpha=a^(-3)

and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its barycentric coordinates are (a^(-2),b^(-2),c^(-2)), thus completing the cyclic permutation of barycentric coordinates for the first Brocard point, namely (b^(-2),a^(-2),c^(-2)), and the second Brocard point, namely (c^(-2),a^(-2),b^(-2)) (Eddy and Fritsch 1994).


See also

Brocard Points, First Brocard Point, Second Brocard Point

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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. 66, 1893.Eddy, R. H. and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle." Math. Mag. 67, 188-205, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(76)=3rd Brocard Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X76.

Referenced on Wolfram|Alpha

Third Brocard Point

Cite this as:

Weisstein, Eric W. "Third Brocard Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThirdBrocardPoint.html

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