cos(A/3) + 2 cos(B/3) cos(C/3) :
cos(B/3) + 2 cos(C/3) cos(A/3) :
cos(C/3) + 2 cos(A/3) cos(B/3).
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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) : |
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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.
