Kosnita point

Kosnita theorem with Kosnita point K

The Kosnita point , named after the Romanian mathematician Cezar Coșniță (1910–1962), is one of the special points of a triangle . It is isogonally conjugated to the center of the Feuerbach circle .

The period derives its name from Kosnita's sentence , which says the following:

"Let O be the circumcenter of a triangle ABC and M _AB , M _BC and M _AC the circumcenter of the triangles OBC, AOC and ABO, then the straight lines CM _AB , AM _BC and BM _AC intersect at a common point."

The common intersection of the straight lines from Kosnita's theorem is called the Kosnita point , it has the Kimberling number X (54).

Coordinates

The barycentric coordinates of the Kosnita point are

${\displaystyle {\frac {\sin \alpha }{\cos(\beta -\gamma )}}\,:\,{\frac {\sin \beta }{\cos(\gamma -\alpha )}}\,:\,{\frac {\sin \gamma }{\cos(\alpha -\beta )}}.}$

literature

• Darij Grinberg: On the Kosnita Point and the Reflection Triangle (PDF) Forum Geometricorum, Volume 3, 2003, pp. 105-111.

Web links

• Eric W. Weisstein : Kosnita Point . In: MathWorld (English).
• X (54) in the Encyclopedia of Triangle Centers