The Euler Circle

U ovom radu proučavana je jedna kružnica pridružena trokutu. Kružnica na kojoj leže polovišta stranica trokuta, nožišta visina te polovišta dužina kojima je jedna krajnja točka vrh trokuta, a druga ortocentar trokuta poznata je kao Eulerova kružnica ili kružnica devet točaka. Važna svojstva ove kružnice su istražena. Dokazana je i tvrdnja koja povezuje Eulerovu kružnicu, trokutu upisanu kružnicu i trokutu pripisane kružnice, poznati Feuerbachov teorem.In this paper, a circle that is joined to the triangle is studied. The circle which passes through the mid-points of the sides of a triangle, the feett of the altitudes and the mid-points of the line segments from the orthocenter to the vertices of a triangle is called Euler circle or the nine-point circle. Some important characteristics of this circle are researched. The assertion that links Euler circle to the inscribed and escribed circles of a triangle was proved. It is well known Feuerbach’s theorem