bisected perimeter point

Let T_1 be the point at which the J_1-excircle meets the side A_2 A_3 of a triangle Δ A_1 A_2 A_3, and define T_2 and T_3 similarly. Then the lines A_1 T_1, A_2 T_2, and A_3 T_3 concur in the Nagel point Na (sometimes denoted M). The Nagel point has triangle center function α = (b + c - a)/a and is Kimberling center X_8. The triangle Δ T_1 T_2 T_3 is called the extouch triangle, and its is therefore the Cevian triangle with respect to the Nagel point.

cleavance center | excenter | excentral triangle | excircles | Fuhrmann circle | Gergonne point | mittenpunkt | Nagel line | splitter | trisected perimeter point