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[[Image:Extouch Triangle and Nagel Point.svg|right|frame|325px|The extouch triangle (red, ΔT<sub>A</sub>T<sub>B</sub>T<sub>C</sub>) and the [[Nagel point]] (blue, N) of a triangle (black, ΔABC). The orange circles are the [[excircles]] of the triangle.]]
In [[geometry]], the '''extouch triangle''' of a [[triangle]] is formed by joining the points at which the three [[excircle]]s touch the triangle.
==Coordinates== The [[vertex (geometry)|vertices]] of the extouch triangle are given in [[trilinear coordinates]] by: :<math>T_A = 0 : \csc^2{\left( B/2 \right)} : \csc^2{\left( C/2 \right)}</math>
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:<math>T_C = \frac{-a+b+c}{a} : \frac{a-b+c}{b} : 0</math>
==Related figures==
The intersection of the lines connecting the vertices of the original triangle to the corresponding vertices of the extouch triangle is the [[Nagel point]]. This is shown in blue and labelled "N" in the diagram.
The [[Mandart inellipse]] is tangent to the sides of the triangles at the three vertices of the extouch triangle.<ref>{{citation
| last = Juhász | first = Imre
| journal = Annales Mathematicae et Informaticae
| mr = 3005114
| pages = 37–46
| title = Control point based representation of inellipses of triangles
| url = http://ami.ektf.hu/uploads/papers/finalpdf/AMI_40_from37to46.pdf
| volume = 40
| year = 2012}}.</ref>
==Area==
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