TOPICS

# Kosnita Point

The point Ko of concurrence in Kosnita theorem, i.e., the point of concurrence of the lines connecting the vertices , , and of a triangle with the circumcenters of the triangles , , and (where is the circumcenter of ). 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 (Kimberling 1998, p. 75; note spelling correction).

Kosnita Theorem, Triangulation Point

## References

de Villiers, M. "A Dual to Kosnita's Theorem." Math. and Informatics Quart. 6, 169-171, 1996. http://mzone.mweb.co.za/residents/profmd/kosnita.htm.Grinberg, D. "On the Kosnita Point and the Reflection Triangle." Forum Geom. 3, 105-111, 2003. http://forumgeom.fau.edu/FG2003volume3/FG200311index.html.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(54)=Kosnita Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X54.Musselman, 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.

Kosnita Point

## Cite this as:

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