## X(3120) (DANNEELS PERSPECTOR FOR X(10))

 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) = bc(b + c)(b - c)2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3120) lies on these lines:
1,149    2,846    7,2648    11,244    27,2206    31,1836    38,2886    42,226    58,79    109,2006    115,125    225,1042    321,2887    334,1978    442,2292    516,902    614,990    726,3006    851,1284    899,908    946,1201    986,2476    1109,2632    1365,2611    1834,2650    2170,2969

X(3120) = reflection of X(902) in X(3011)
X(3120) = X(I)-Ceva conjugate of X(J) for these I,J: 10,523    27,649    79,513    86,514    226,661    313,1577    1086,3125
X(3120) = cevapoint of X(115) and X(2643)
X(3120) = X(2643)-cross conjugate of X(3125)
X(3120) = crosspoint of X(I) and X(J) for these I,J: 10,523    65,513    86,514    313,1577    321,693    1086,1111
X(3120) = crosssum of X(I) and X(J) for these I,J: 21,100    42,101    58,110    163,2206    692,1333    1110,1252
X(3120) = crossdifference of every pair of points on the line X(101)X(110)

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