Kosnita Point


The point Ko of concurrence in Kosnita theorem, i.e., the point of concurrence of the lines connecting the vertices A, B, and C of a triangle DeltaABC with the circumcenters of the triangles DeltaBCO, DeltaCAO, and DeltaABO (where O is the circumcenter of DeltaABC). The point was so named by Rigby (1997), and is the isogonal conjugate of the nine-point center (Grinberg 2003).

The Kosnita point has triangle center function


and is Kimberling center X_(54) (Kimberling 1998, p. 75; note spelling correction).

See also

Kosnita Theorem, Triangulation Point

Explore with Wolfram|Alpha


de Villiers, M. "A Dual to Kosnita's Theorem." Math. and Informatics Quart. 6, 169-171, 1996., D. "On the Kosnita Point and the Reflection Triangle." Forum Geom. 3, 105-111, 2003., C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(54)=Kosnita Point.", J. R. and Goormaghtigh, R. "Advanced Problem 3928." Amer. Math. Monthly 46, 601, 1939.Musselman, J. R. and Goormaghtigh, R. "Solution to Advanced Problem 3928." Amer. Math. Monthly 48, 281-283, 1941.Rigby, J. "Brief Notes on Some Forgotten Geometrical Theorems." Math. and Informatics Quart. 7, 156-158, 1997.

Referenced on Wolfram|Alpha

Kosnita Point

Cite this as:

Weisstein, Eric W. "Kosnita Point." From MathWorld--A Wolfram Web Resource.

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