auxiliary triangle

The triangle Δ M_A M_B M_C formed by joining the midpoints of the sides of a triangle Δ A B C. The medial triangle is sometimes also called the auxiliary triangle. The medial triangle is the Cevian triangle of the triangle centroid G and the pedal triangle of the circumcenter O. It is also the cyclocevian triangle of the orthocenter H. The medial triangle is the polar triangle of the Steiner inellipse.

anticomplementary triangle | circum-medial triangle | cleavance center | cleaver | median triangle | nine-point circle | Spieker center | Spieker circle | Steiner inellipse | triangle median