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EulerLine

Among 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.