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

### 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 ...

... 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**...

### Famous quotes containing the word system:

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

—G.C. (Georg Christoph)