## X(241) (X(1)-LINE CONJUGATE OF X(55))

 Interactive Applet

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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 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) = cos4B/2 - [cos2(A/2)][cos2(B/2) +cos2(C/2)] + cos4(C/2)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(241) lies on these lines: 1,3    2,85    6,77    7,37    9,269    44,651    63,220    141,307    218,222    239,664    277,278    294,910    347,1108    514,650    960,1042

X(241) = isogonal conjugate of X(294)
X(241) = crosssum of X(I) and X(J) for these (I,J): (6,910), (518,1376
X(241) = crossdifference of any two points on line X(55)X(650)
X(241) = X(1)-Hirst inverse of X(57)
X(241) = X(1)-line conjugate of X(55)
X(241) = X(I)-beth conjugate of X(J) for these (I,J): (2,241), (100,241), (1025,241), (1026,241)

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