its nine-point center. Thus, the nine-point center forms the center of a point reflection that maps the medial triangle to the Euler triangle, and vice versa. According to Lester's theorem, the nine-point center lies on a common circle with three other points: the two Fermat points and the circumcenter. The Kosnita point of a triangle, a triangle center associated with Kosnita's theorem, is the isogonal conjugate of the nine-point center. Coordinates Trilinear coordinates for the nine-point center are The barycentric coordinates of the nine-point center are Thus if and only if two of the vertex angles differ from each other by more than 90°, one of the barycentric coordinates is negative and so the nine-point center is outside the triangle. References External links Triangle centers