## X(105) (Λ(INCENTER, SYMMEDIAN POINT))

 Interactive Applet

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/[b2 + c2 - a(b + c)] : 1/[c2 + a2 - b(c + a)] : 1/[a2 + b2 - c(a + b)]
Barycentrics    a/[b2 + c2 - a(b + c)] : b/[c2 + a2 - b(c + a)] : c/[a2 + b2 - c(a + b)]

X(105) = Λ(X(1), X(6))
X(105) = Ψ(X(101), X(1))

X(105) lies on these lines:
1,41    2,11    3,277    6,1002    21,99    25,108    28,112    31,57    56,279    81,110    88,901    104,885    106,1022    165,1054    238,291    330,932    513,840    644,1083    659,884    666,898    825,985    910,919    961,1104

X(105) = reflection of X(I) in X(J) for these (I,J): (644,1083), (1292,3)
X(105) = isogonal conjugate of X(518)
X(105) = anticomplement of X(120)
X(105) = cevapoint of X(1) and X(238)
X(105) = X(1)-Hirst inverse of X(294)
X(105) = X(I)-beth conjugate of X(J) for these (I,J): (21,101), (927,105)

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