## X(3125) (DANNEELS PERSPECTOR FOR X(81))

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c)(b - c)2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3125) lies on these lines:
1,1929    6,1718    10,762    37,1018    38,1573    65,213    115,125    244,665    257,274    335,668    614,1572    758,2238    910,2251    918,1086    1333,2160    1411,1415    1575,1739    2092,2294    2642,2643

X(3125) = X(I)-Ceva conjugate of X(J) for these I,J: 28,667    37,661    65,512    81,513    244,3122    257,514    274,2530    321,523    1086,3120    2160,649

X(3125) = cevapoint of X(2643) and X(3124)
X(3125) = X(I)-cross conjugate of X(J) for these I,J: 2643,3120    3124,3122
X(3125) = crosspoint of X(I) and X(J) for these I,J: 10,514    37,661    81,513    244,1086    321,523    649,1400    1880,2501
X(3125) = crosssum of X(I) and X(J) for these I,J: 37,100    58,101    72,906    81,662    110,1333    190,333    643,2287    692,2205    765,1252    1331,2327

X(3125) = crossdifference of every pair of points on the line X(100)X(110)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.

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Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense