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 Mandart inellipse is tangent to the sides of the reference triangle at the three vertices of the extouch triangle.^{[1]}

Area

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The area of the extouch triangle, K_{T}, is given by:

$K_{T}=K{\frac {2r^{2}s}{abc}}$

where K and r are the area and radius of the incircle, s is the semiperimeter of the original triangle, and a, b, c are the side lengths of the original triangle.

^Juhász, Imre (2012), "Control point based representation of inellipses of triangles" (PDF), Annales Mathematicae et Informaticae, 40: 37–46, MR 3005114.

^Weisstein, Eric W. "Extouch Triangle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ExtouchTriangle.html