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Bicentric Points

Bicentric points P and P^' are a pair in which P and P^' have respective trilinear coordinates alpha:beta:gamma=f(a,b,c):f(b,c,a):f(c,ab) and alpha^':beta^':gamma^'=f(a,c,b):f(b,a,c):f(c,b,a) for some homogeneous function f such that |f(a,c,b)|!=|f(a,b,c)|.

The best-known example of a pair of bicentric points are the first and second Brocard Points Omega and Omega^', which have trilinear coordinates c/b:a/c:b/a and b/c:c/a:a/b, respectively (Kimberling 1998, pp. 47-48).

See also

Brocard Points, First Brocard Point, Second Brocard Point

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Bicentric Pair of Points and Related Triangle Centers." Forum Geom. 3, 35-47, 2002. https://web.archive.org/web/20231028180348/https://forumgeom.fau.edu/FG2003volume3/FG200303index.html.Kimberling, C. "Bicentric Pairs of Points." https://faculty.evansville.edu/ck6/encyclopedia/BicentricPairs.html.

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Bicentric Points

Cite this as:

Weisstein, Eric W. "Bicentric Points." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BicentricPoints.html

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