## X(3057) (INTERSECTION OF LINES X(1)X(3) AND X(10)X(11))

 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 - a)(b2 + c2 - 2bc + ab + ac)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3057) lies on these lines:
1,3    4,1000    8,210    10,11    12,946    19,2256    21,643    33,1829    34,1902    37,1953    45,374    72,519    140,1387    144,145    190,1222    200,2136    219,2264    220,2082    227,1457    278,1888    355,1479    388,962    496,1737    595,2361    614,1616    1212,1334    1317,1364    2809,3021

X(3057) = reflection of X(I) in X(J) for these (I,J): (8,960)    (65,1)
X(3057) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,1201)    (190,650)    (1293,513)
X(3057) = cevapoint of X(1) and X(2943)
X(3057) = crosspoint of X(1) and X(8)
X(3057) = crosssum of X(I) and X(J) for these (I,J): (56,269)    (1,56)    (55,1743)

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