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.