Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst (2008). "Orthocentric simplices and biregularity". Results in Mathematics52 (1–2): 41–50. doi:10.1007/s00025-008-0294-4. "It is well known that the incenter of a Euclidean triangle lies on its Euler line connecting the centroid and the circumcenter if and only if the triangle is isosceles.".