Morley's triangle

The first Morley triangle Δ A' B' C', also simply known as "Morley's triangle", is the triangle constructed from pairwise intersections of the angle trisectors of a given triangle Δ A B C. In particular, its A'-vertex is the point of intersection of the first trisector of B when swinging B C counterclockwise about B and the first trisector of C, with the B'- and C'-vertices similarly defined. By Morley's theorem, this triangle is equilateral.

first Morley adjunct triangle | Marion's theorem | Morley's theorem | second Morley triangle | third Morley triangle