HYACINTHOS 26323

[Antreas P. Hatzipolakis]:

 

In the McCay's cubic entry K003 in CTC , are listed the following triangle centers lying on the cubic:

X(1), X(3), X(4), X(1075), X(1745), X(3362), E(412)=X(1075)*

The last one is the isogonal conjugate of X(1075) not listed in ETC.

In order to be included in ETC: Which are its properties (lines it is lying on, etc) ?

[César Lozada]:

X(1075)* = Isogonal conjugate of X(1075)

= (S^2-SB*SC)/(16*R^4-8*(SB+SC)* R^2-S^2-2*SA^2+SW^2) : :  (barycentrics)

= cos(A)/((2*cos(A)+2*cos(3*A))* cos(B-C)+cos(2*(B-C))-3*cos(2* A)-2) : :  (trilinears)

= On McCay cubic(K003) and these lines: {3,1075}, {577,6759}, {1092,2055}

= Isogonal conjugate of X(1075)

= X(4)-crossconjugate-of-X(3)

= [ 1.303070197580847, 1.35587259452337, 2.100566440661658 ]

 

César Lozada