The extouch triangle Δ T_1 T_2 T_3 is the triangle formed by the points of tangency of a triangle Δ A_1 A_2 A_3 with its excircles J_1, J_2, and J_3. The points T_1, T_2, and T_3 can also be constructed as the points which bisect the perimeter of Δ A_1 A_2 A_3 starting at A_1, A_2, and A_3. It is the Cevian triangle of the Nagel point, the pedal triangle of the Bevan point X_40, and the cyclocevian triangle of X_189. It is the polar triangle of the Mandart inellipse.

Cevian triangle | excenter | excircles | Mandart circle | Mandart inellipse | Nagel point