The perspector of the first Morley triangle with reference triangle 
is called the second Morley center.
Its triangle center function is
 |
which is Kimberling center 
.
Second Morley Center
See also
First Morley Center, Morley CentersExplore with Wolfram|Alpha
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://faculty.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.Taylor, F. G. and Marr, W. L. "The Six Trisectors of Each of the Angles of a Triangle." Proc. Edinburgh Math. Soc. 33, 119-131, 1913-14.Referenced on Wolfram|Alpha
Second Morley CenterCite this as:
Weisstein, Eric W. "Second Morley Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SecondMorleyCenter.html