## X(192) (X(1)-CEVA CONJUGATE OF X(2))

 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

(CONGRUENT PARALLELIANS POINT) Trilinears           bc(ca + ab - bc) : ca(ab + bc - ca) : ab(bc + ca - ab)
Barycentrics    ca + ab - bc : ab + bc - ca : bc + ca - ab

Segments through X(192) parallel to the sidelines with endpoints on the sidelines have equal length. For references as early as 1881, see Hyacinthos message 2929 (Paul Yiu, May 29, 2001). See also

Sabrina Bier, "Equilateral Triangles Intercepted by Oriented Parallelians," Forum Geometricorum 1 (2001) 25-32.

X(192) lies on these lines:
1,87    2,37    6,190    7,335    8,256    9,239    55,385    69,742    144,145    315,746    869,1045

X(192) = reflection of X(I) in X(J) for these (I,J): (8,984), (75,37), (1278,75)
X(192) = isogonal conjugate of X(2162)
X(192) = isotomic conjugate of X(330)
X(192) = complement of X(1278)
X(192) = anticomplement of X(75)
X(192) = X(1)-Ceva conjugate of X(2)
X(192) = crosspoint of X(1) and X(43)
X(192) = crosssum of X(1) and X(87)
X(192) = X(9)-Hirst inverse of X(239)
X(192) = X(646)-beth conjugate of X(192)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense