## X(104) (ANTIPODE OF X(100))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(-1 + cos B + cos C) : 1/(-1 + cos C + cos A) : 1/(-1 + cos C + cos B)
Barycentrics    a/(-1 + cos B + cos C) : b/(-1 + cos C + cos A) : c/(-1 + cos C + cos B)

X(104) = circumcircle-antipode of X(100)
X(104 is the point of intersection, other than A, B, and C, of the circumcircle and Feuerbach hyperbola
X(104) = Λ(X(1), X(3))
X(104) = Ψ(X(101), X(9)).

X(104) lies on these lines:
1,109    2,119    3,8    4,11    7,934    9,48    20,149    21,110    28,107    36,80    55,1000    79,946    99,314    105,885    112,1108    256,1064    294,919    355,404    376,528    513,953    517,901    631,958

X(104) = midpoint of X(20) and X(149)
X(104) = reflection of X(I) in X(J) for these (I,J): (4,11), (100,3), (153,119), (1537,1387)
X(104) = isogonal conjugate of X(517)
X(104) = complement of X(153)
X(104) = anticomplement of X(119)
X(104) = cevapoint of X(I) and X(J) for these (I,J): (1,36), (44,55)
X(104) = X(21)-beth conjugate of X(109)

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