A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as illustrated above. The incenter and excenters of a triangle are an orthocentric system. The centers of the circumcircles of the points in an orthocentric system form another orthocentric system congruent to the first, and are the reflection of the original points in their common nine-point center. The centroids of the points in an orthocentric system form another orthocentric system similar to the first, but one third the size.

angle bisector | circumcircle | cyclic quadrangle | Johnson's theorem | Johnson triangle | Johnson-Yff circles | nine-point circle | orthic triangle | orthocenter | orthocentric quadrangle | orthocentric quadrilateral | polar circle | rectangular hyperbola