Editing Incircle and excircles (section)

===Incentral and excentral triangles===
The points of intersection of the interior angle bisectors of <math>\triangle ABC</math> with the segments <math>BC</math>, <math>CA</math>, and <math>AB</math> are the vertices of the '''incentral triangle'''. Trilinear coordinates for the vertices of the incentral triangle <math>\triangle A'B'C'</math> are given by{{Citation needed|date=May 2020}}
:<math display=block>\begin{array}{ccccccc}
  A' &=& 0 &:& 1 &:& 1 \\[2pt]
  B' &=& 1 &:& 0 &:& 1 \\[2pt]
  C' &=& 1 &:& 1 &:& 0
\end{array}</math>

The '''excentral triangle''' of a reference triangle has vertices at the centers of the reference triangle's excircles. Its sides are on the external angle bisectors of the reference triangle (see figure at [[#top|top of page]]). Trilinear coordinates for the vertices of the excentral triangle <math>\triangle A'B'C'</math> are given by{{Citation needed|date=May 2020}}
:<math display=block>\begin{array}{ccrcrcr}
  A' &=& -1 &:& 1 &:& 1\\[2pt]
  B' &=& 1 &:& -1 &:& 1 \\[2pt]
  C' &=& 1 &:& 1 &:& -1
\end{array}</math>