If the tetrahedron's altitudes do intersect, then the Monge point and the orthocenter coincide to give the class of orthocentric tetrahedron.
12.
The common nine-point circle is tangent to all 16 incircles and excircles of the four triangles whose vertices form the orthocentric system.
13.
Four of these points are the original orthocentric points and the additional three points are the orthogonal intersections at the feet of the altitudes.
14.
If four points form an orthocentric system, then " each " of the four points is the orthocenter of the other three.
15.
The four possible triangles have a set of four Brianchon point, H, the orthocentric point closest to the common nine-point center.
16.
If the six connectors that join any pair of orthocentric points are extended to six lines that intersect each other, they generate seven intersection points.
17.
This relationship between the orthic triangle and the original four orthocentric points leads directly to the fact that the incenter and excenters of a reference triangle form an orthocentric system.
18.
This relationship between the orthic triangle and the original four orthocentric points leads directly to the fact that the incenter and excenters of a reference triangle form an orthocentric system.
19.
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 equations
20.
Four points forming non-adjacent vertices of a rhombohedron necessarily form the four vertices of an orthocentric tetrahedron, and all orthocentric tetrahedra can be formed in this way.
