INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

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


Click here to access the list of all triangle centers.

Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon Run Macro Tool, select the center name from the list and, then, click on the vertices A, B and C successively.

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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           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.

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



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