Extouch Triangle

The extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle. The vertices of the extouch triangle are given in trilinear coordinates by:

Or, equivalently, where a,b,c are the lengths of the sides opposite angles A, B, C respectively,

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.