Circumcenter: The point at which the perpendicular bisectors of the sides of a triangle intersect and which is equidistant from the three vertices. Orthocenter: The orthocenter is one of the triangle's points of concurrency formed by the intersection of the triangle's 3 altitudes. These three altitudes are always concurrent. Centroid: The center of mass of a geometric object of uniform density. Euler has contributed many discoveries to the mathematical world including Euler's number and Euler's line which we will discuss below. Euler's Line: In any triangle, three remarkable points - circumcenter, centroid, and orthocenter - are collinear, that is, lie on the same line, Euler's line. Centroid is always located between the circumcenter and the orthocenter twice as close to the former as to the latter.