Orthocentric system
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In geometry, an orthocentric system is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three.
If four points form an orthocentric system, then each of the four points is the orthocenter of the other three. These four possible triangles will all have the same nine point circle.
The centers of the incircle and excircles of a triangle form an orthocentric system.