The second Morley triangle is made by rotating line 
toward vertex 
about vertex 
by angle 
. It is an equilateral
triangle.
It has trilinear vertex matrix
![[1 2cos[1/3(C-2pi)] 2cos[1/3(B-2pi)]; 2cos[1/3(C-2pi)] 1 2cos[1/3(A-2pi)]; 2cos[1/3(B-2pi)] 2cos[1/3(A-2pi)] 1]](/images/equations/SecondMorleyTriangle/NumberedEquation1.svg) |
(1)
|
(Kimberling 1998, p. 165).
Its signed side lengths 
are
![s^'=8Rsin[1/3(A-2pi)]sin[1/3(B-2pi)]sin[1/3(C-2pi)],](/images/equations/SecondMorleyTriangle/NumberedEquation2.svg) |
(2)
|
giving an area of
![A=16sqrt(2)R^2sin^2[1/3(A-2pi)]sin^2[1/3(B-2pi)]sin^2[1/3(C-2pi)].](/images/equations/SecondMorleyTriangle/NumberedEquation3.svg) |
(3)
|
The following table lists perspectors of the second Morley triangles with other named triangles that are Kimberling centers.
| triangle | Kimberling | perspector |
| first Morley triangle |  | second Morley-Taylor-Marr center |
| reference triangle |  | 5th Morley-Taylor-Marr center |
| third Morley triangle |  | 6th Morley-Taylor-Marr center |
