In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle.
Let
A
B
C
be an arbitrary triangle,
O
its circumcenter and
O
a
,
O
b
,
O
c
are the circumcenters of three triangles
O
B
C
,
O
C
A
, and
O
A
B
respectively. The theorem claims that the three straight lines
A
O
a
,
B
O
b
, and
C
O
c
are concurrent. This result has been 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
X
(
54
)
in Clark Kimberling's list. This theorem is special case of Dao's theorem on six circumcenters associated with a cyclic hexagon in.
