In geometry, the Nagel point is a point associated with any triangle. Given a triangle ABC, let TA, TB, and TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively. The lines ATA, BTB, CTC concur in the Nagel point N of triangle ABC. The Nagel point is named after Christian Heinrich von Nagel, a nineteenth century German mathematician, who wrote about it in 1836.
Another construction of the point TA is to start at A and trace around triangle ABC half its perimeter, and similarly for TB and TC. Because of this construction, the Nagel point is sometimes also called the bisected perimeter point, and the segments ATA, BTB, CTC are called the triangle's splitters.
Read more about Nagel Point: Relation To Other Triangle Centers, Trilinear Coordinates, See Also
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