EulerLineAmong the best known triangle centers are the centroid (G), circumcenter (O), orthocenter (H), and nine-point-center (N). In the plane of any triangle, these four points all lie on a line. It is known as the Euler line. In fact, more more is true: the distance ratio for each pair of these points remain constant as the shape of the triangle changes. Several such ratios are printed above.
For more, see GEOMETRY IN ACTION, Chapter 1.