Or, equivalently, where a,b,c are the lengths of the sides opposite angles A, B, C respectively,
The triangle's splitters are lines connecting the vertices of the original triangle to the corresponding vertices of the extouch triangle; they bisect the triangle's perimeter and meet at the Nagel point. This is shown in blue and labelled "N" in the diagram.
The area of the extouch triangle, , is given by:
This is the same area as the intouch triangle.
- Juhász, Imre (2012), "Control point based representation of inellipses of triangles" (PDF), Annales Mathematicae et Informaticae, 40: 37–46, MR 3005114<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.