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:
“Short of a wholesale reform of college athletics—a complete breakdown of the whole system that is now focused on money and power—the women’s programs are just as doomed as the men’s are to move further and further away from the academic mission of their colleges.... We have to decide if that’s the kind of success for women’s sports that we want.”
—Christine H. B. Grant, U.S. university athletic director. As quoted in the Chronicle of Higher Education, p. A42 (May 12, 1993)