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

References

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.'' http://cedar.evansville.edu/~ck6/tcenters/recent/morley.html.

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