## X(3201) (X(54)-CEVA CONJUGATE OF X(16))

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z), where x : y : z = X(54) and u : v : w = X(16)

Trilinears            sin(A - π/3) sin(2A - 2π/3) : sin(B - π/3) sin(2B - 2π/3) : sin(C - π/3) sin(2C - 2π/3)      (M. Iliev, 4/12/07)
Trilinears            cos 3A + cos(A - π/3) : cos 3B + cos(B - π/3) : cos 3C + cos(C - π/3)      (M. Iliev, 4/12/07)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b), where f(a,b,c) = u(-u/x + v/y + w/z)

X(3201) lies on these lines:
3,3206    6,3200    14,110    15,184    17,54    49,61    62,1147    203,215    3104,3202

X(3201) = X(I)-Ceva conjugate of X(J) for these I,J: 54,16    2981,50
X(3201) = crosspoint of X(16) and X(61)
X(3201) = crosssum of X(14) and X(17)

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