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Second Brocard Point

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BrocardPoints

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ∠Omega^'AC, ∠Omega^'CB, and ∠Omega^'BA are equal, with the unique such angle denoted omega^'. omega^' is equal to the Brocard angle omega.

Omega^' fails to be a triangle center because it is bicentric with the first Brocard point Omega, but it has trilinear coordinates

b/c:c/a:a/b

(Kimberling 1998, p. 47).

Note that extreme care is needed when consulting the literature, since reversing the order in which the points of the triangle are labeled results in exchanging the Brocard points.

See also

Brocard Angle, Brocard Midpoint, Brocard Points, First Brocard Point, Third Brocard Point

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References

Honsberger, R. "The Brocard Points." Ch. 10 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 98-124, 1995.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Lemoine, É. "Propriétés relatives a deux points Omega, Omega^' du plan d'un triangle ABC qui se déduisent d'un point K quelconque di plan comme les points de Brocard de déduisent du point de Lemoine." Mathesis 6, Suppl. 3, 1-22, 1886.

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Second Brocard Point

Cite this as:

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

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