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. [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 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. [6] [7] [8] [9] [10] [11] [12]
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. [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 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. [6] [7] [8] [9] [10] [11] [12]