Draw a triangle Δ A_1 A_2 A_3, and let A_1^, be the intersection of the parallel to A_3 A_1 through A_2 (the A_2-exmedian) and the parallel to A_1 A_2 through A_3 (the A_3-exmedian). Then A_1^, is the A_1-exmedian point of the triangle Δ A_1 A_2 A_3. A triangle Δ A_1 A_2 A_3 has three exmedian points. They are the vertices of the anticomplementary triangle of Δ A_1 A_2 A_3.

anticomplementary triangle | exmedian