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Morley Centers

The Centroid of Morley's Triangle is called Morley's first center. It has Triangle Center Function

\alpha=\cos({\textstyle{1\over 3}} A)+2\cos({\textstyle{1\over 3}} B)\cos({\textstyle{1\over 3}} C).

The Perspective Center of Morley's Triangle with reference Triangle $ABC$ is called Morley's second center. The Triangle Center Function is

\alpha=\sec({\textstyle{1\over 3}} A).

See also Centroid (Geometric), Morley's Theorem, Perspective Center


Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C. ``1st and 2nd Morley Centers.''

Oakley, C. O. and Baker, J. C. ``The Morley Trisector Theorem.'' Amer. Math. Monthly 85, 737-745, 1978.

© 1996-9 Eric W. Weisstein