Nagel Point (Paperback)

High Quality Content by WIKIPEDIA articles In geometry, the Nagel point is a point associated with any triangle. In the plane of a triangle ABC with side lengths a = -BC-, b = -CA-, and c = -AB-, let TA, TB, and TC be the 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.