Kosnita's theorem

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

Let ABC be an arbitrary triangle, O its circumcenter and Oa,Ob,Oc are the circumcenters of three triangles OBC,OCA, and OAB respectively. The theorem claims that the three straight lines AOa, BOb, and COc are concurrent.[1] This result was established by the Romanian mathematician Cezar Coşniţă (1910-1962).[2]

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.[3][4] It is triangle center X(54) in Clark Kimberling's list.[5] 

This theorem is a special case of Dao's theorem on six circumcenters associated with a cyclic hexagon in.

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