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

X(100)
(ANTICOMPLEMENT OF FEUERBACH POINT)


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/(b - c) : 1/(c - a) : 1/(a - b)
                                    = (a - b)(a - c) : (b - c)(b - a) : (c - a)(c - b)

Barycentrics    a/(b - c) : b/(c - a) : c/(a - b)

X(100) = circumcircle-antipode of X(104)
X(100) = Ψ(X(6), X(1))

X(100) lies on these lines:
1,88    2,11    3,8    4,119    6,739    7,1004    9,1005    10,21    20,153    22,197    31,43    32,713    36,519    37,111    40,78    42,81    46,224    56,145    59,521    63,103    72,74    75,675    76,767    92,917    98,228    99,668    101,644    107,823    108,653    109,651    110,643    112,162    144,480    190,659    198,346    213,729    238,899    281,1013    329,972    442,943    484,758    513,765    516,908    517,953    518,840    522,655    560,697    594,1030    645,931    649,660    650,919    658,664    667,898    693,927    731,869    733,893    753,984    756,846    789,874    976,986

X(100) is the {X(10),X(35)}-harmonic conjugate of X(21).

X(100) = midpoint of X(20) and X(153)
X(100) = reflection of X(I) in X(J) for these (I,J): (1,214), (4,119), (8,1145), (80,10), (104,3), (145,1317), (149,11), (962,1537), (1156,9), (1320,1), (1484,140)

X(100) = isogonal conjugate of X(513)
X(100) = complement of X(149)
X(100) = anticomplement of X(11)
X(100) = X(99)-Ceva conjugate of X(190)
X(100) = cevapoint of X(I) and X(J) for these (I,J): (1,513), (3,521), (10,522), (142,514), (442,523)
X(100) = X(I)-cross conjugate of X(J) for these (I,J): (3,59), (513,1), (521,8), (522,21)
X(100) = crosssum of X(I) and X(J) for these (I,J): (1,1054), (244,764), (512,661), (649,663)
X(100) = crossdifference of any two points on line X(244)X(665)
X(100) = X(1)-line conjugate of X(244)

X(100) = X(I)-aleph conjugate of X(J) for these (I,J):
(1,1052), (100,1), (190,63), (643,411), (666,673), (765,100), (1016,190)

X(100) = X(I)-beth conjugate of X(J) for these (I,J):
(8,80), (21,106), (100,109), (333,673), (643,100), (765,100)


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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