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

X(44)
(X(6)-LINE CONJUGATE OF X(1))


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           b + c - 2a : c + a - 2b : a + b - 2c
Barycentrics    a(b + c - 2a) : b(c + a - 2b) : c(a + b - 2c)

X(44) lies on these lines: 1,6    2,89    10,752    31,210    51,209    65,374    88,679    181,375    190,239    193,344    214,1017    241,651    292,660    354,748    513,649    527,1086    583,992    678,902

X(44) is the {X(1),X(9)}-harmonic conjugate of X(45).

X(44) = midpoint of X(190) and X(239)
X(44) = reflection of X(1279) in X(238)
X(44) = isogonal conjugate of X(88)
X(44) = complement of X(320)
X(44) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,214), (88,1), (104,55)
X(44) = crosspoint of X(I) and X(J) for these (I,J): (1,88), (2,80)
X(44) = crosssum of X(I) and X(J) for these (I,J): (1,44), (6,36), (57,1465)
X(44) = crossdifference of any two points on line X(1)X(513)
X(44) = X(6)-line conjugate of X(1)
X(44) = X(88)-cross conjugate of X(44)
X(44) = X(I)-beth conjugate of X(J) for these (I,J): (9,44), (644,44), (645,239), (44,44)

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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