In geometry, an orthocentric system is a set of four points in the plane one of which 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. Consequently these four possible triangles must all have circumcircles with the same circumradius.
Read more about Orthocentric System: The Common Nine-point Circle, The Common Orthic Triangle, Its Incenter and Excenters, The Orthocentric System and Its Orthic Axes, Euler Lines and Homothetic Orthocentric Systems, Further Properties
Famous quotes containing the word system:
“The intellect is vagabond, and our system of education fosters restlessness. Our minds travel when our bodies are forced to stay at home. We imitate; and what is imitation but the travelling of the mind?”
—Ralph Waldo Emerson (1803–1882)