Kosnita's theorem

In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle.

Let be an arbitrary triangle, its circumcenter and are the circumcenters of three triangles , , and respectively. The theorem claims that the three straight lines , , and are concurrent. This result was established by the Romanian mathematician Cezar Coşniţă (1910-1962).

Their point of concurrence is known as the triangle's Kosnita point (named by Rigby in 1997). It is the isogonal conjugate of the nine-point center. It is triangle center in Clark Kimberling's list. This theorem is a special case of Dao's theorem on six circumcenters associated with a cyclic hexagon in.

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