Euler Line

The Euler line is a unique line that intersects several important points in a triangle. The circumcenter (intersection of the perpendicular bisectors), the centroid (the intersection of the mediums), and the orthocenter (the intersection of the altitudes). The incenter (intersection of the angle bisectors) will only lie on the line if the triangle is an isosceles and all of the intersections mentioned will be the same point if the triangle is an equilateral.