More Vector Formulas in A General Tetrahedron
If OABC forms a general tetrahedron with a vertex O as the origin and vectors a, b and c represent the positions of the vertices A, B, and C with respect to O, then the radius of the insphere is given by:
and the radius of the circumsphere is given by:
which gives the radius of the twelve-point sphere:
where:
In the formulas throughout this section, the scalar a2 represents the inner vector product a·a; similarly b2 and c2.
The vector positions of various centers are as follows:
The centroid
The incenter
The circumcenter
The Monge point
The Euler line relationships are:
where T is twelve-point center.
Also:
and:
Read more about this topic: Tetrahedron
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