Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.

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