Let △DEF be the triangle formed by the intersections of the adjacent angle trisectors of triangle △ABC. △DEF is called the Morley triangle of △ABC. Morley's trisector theorem states that the Morley triangle of any triangle is always an equilateral triangle.
First Morley center
Let △DEF be the Morley triangle of △ABC. The centroid of △DEF is called the first Morley center of △ABC.[1][3]
Second Morley center
Let △DEF be the Morley triangle of △ABC. Then, the lines AD, BE, CF are concurrent. The point of concurrence is called the second Morley center of triangle △ABC.[1][3]