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:
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)