nL-n-P3: nL-Morley’s Circumcenter / Centric Center

A Triangle (3-Line) has a circumcircle. Morley in Ref-49 calls this circle a Centercircle.
In a Quadrilateral (4-Line) there are 4 component 3-Lines whose 3L-Centercircle Centers are concyclic on the 4L-Centercircle.
In a Pentalateral (5-Line) there are 5 component 4-Lines whose 4L-Centercircle Centers are concyclic on the 5L-Centercircle. Etc.
Morley proved in Ref-49 that there exists a Centercircle in an n-Line for all n, built from the centers of the Centercircles from the Component m-Lines.
The Center of this Centercircle is shortly named the Centric Center by Goormaghtigh in Ref-55.
This nL-Centric Center is the basis for several other Morley points.
Morley uses the letter “a1“ or “p0“ for this point in Ref-49.
Morley describes in Ref-49 some recursive points “pi“ for i=1, .. , n/2 (see nL-n-pi) that are useful for constructing some other points. In this notation nL-n-P3 = p0 (or in EPG notation: nL-n-p0).

nL nP3 Figure 01
Correspondence with ETC/EQF:
When n=3, then nL-n-P3 = X(3).
When n=4, then nL-n-P3 = QL-P4.
• 5L-n-P3 is the ratiopoint 5L-s-P4.5L-s-P5 (3:-2).