The famous Morley Theorem states that the three points of intersection of the adjacent trisectors of the angles of a triangle ABC form an equilateral triangle. In 1967, Peter Yff proved that the center of the Morley triangle, called the 1st Morley center, is given by trilinear coordinates
cos(A/3) + 2 cos(B/3) cos(C/3) : |

sec(A/3) : sec(B/3) : sec(C/3)

For an introduction to the Morley triangles and 150 further references on these remarkable objects, see

**Cletus O. Oakley and Justine C. Baker**, "The Morley trisector theorem," *Amer. Math. Monthly* 85 (1978) 737-745.

(For a quick lesson on trilinears, click on TRILINEAR COORDINATES.)

Biographical Sketch of Frank Morley

Triangle Centers

Clark Kimberling Home Page