Extouch triangle

Triangle formed from the points of tangency of a given triangle's excircles

Arbitrary triangle $△ ABC$

  Excircles, tangent to the sides of $△ ABC$ at $T A, T B, T C$

  Extouch triangle $△ T A T B T C$

  Splitters of the perimeter $AT A, BT B, CT C$ ; intersect at the Nagel point $N$

In Euclidean geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle.