# Orthocentric System

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.

### Other articles related to "orthocentric system, orthocentric, system":

Orthocentric System - Further Properties
... The four Euler lines of an orthocentric system are orthogonal to the four orthic axes of an orthocentric system ... The six connectors that join any pair of the original four orthocentric points will produce pairs of connectors that are orthogonal to each other such that they satisfy the distance ... to all four possible triangles in an orthocentric system it is tangent to 16 circles comprising the incircles and excircles of the four possible triangles ...
Other Properties of The Nine-point Circle
... If an orthocentric system of four points A, B, C and H is given, then the four triangles formed by any combination of three distinct points of that system all share the ... and P be an arbitrary point in the plane of the orthocentric system ... The centers of the incircle and excircles of a triangle form an orthocentric system ...

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Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates.
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