Kosnita's theorem
Geometric theorem regarding circles and triangles
From Wikipedia, the free encyclopedia
In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle.
Triangle △ABC
Circumcircle (centered at circumcenter O)
AOa, BOb, COc (concur at Kosnita point)
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 asserts 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]
