Loterre: Mathématiques: Kosnita's theorem

geometry > Euclidean geometry > Kosnita's theorem

Kosnita's theorem

In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle. Let ${\\displaystyle ABC}$ be an arbitrary triangle, ${\\displaystyle O}$ its circumcenter and ${\\displaystyle O_{a},O_{b},O_{c}}$ are the circumcenters of three triangles ${\\displaystyle OBC}$ , ${\\displaystyle OCA}$ , and ${\\displaystyle OAB}$ respectively. The theorem claims that the three straight lines ${\\displaystyle AO_{a}}$ , ${\\displaystyle BO_{b}}$ , and ${\\displaystyle CO_{c}}$ are concurrent. This result was established by the Romanian mathematician Cezar Coşniţă (1910-1962).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Kosnita%27s_theorem)