The Stammler triangle is the triangle formed by the centers of the Stammler circles. It is an equilateral triangle. It circumscribes the circumcircle and homothetic to the first Morley triangle. The points of contact of this triangle and the circumcircle form the circumtangential triangle. It has trilinear vertex matrix [cos A - 2cos((B - C)/3) | cos B + 2cos((B + 2C)/3) | cos C + 2cos((2B + C)/3) cos A + 2cos((A + 2C)/3) | cos B - 2cos((C - A)/3) | cos C + 2cos((2A + C)/3) cos A + 2cos((A + 2B)/3) | cos B + 2cos((2A + B)/3) | cos C - 2cos((A - B)/3)]. The circumcircle of the Stammler triangle is the Stammler circle.

proportionally-cutting circle | Stammler circle | Stammler circles | Stammler hyperbola