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

X(524)
(ISOGONAL CONJUGATE OF X(111))


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           (2a2 - b2 - c2)/a : (2b2 - c2 - a2)/b : (2c2 - a2 - b2)/c
Barycentrics    2a2 - b2 - c2 : 2b2 - c2 - a2 : 2c2 - a2 - b2

As the isogonal conjugate of a point on the circumcircle, X(524) lies on the line at infinity.

X(524) lies on these lines: 2,6    5,576    30,511    53,317    67,858    76,598    99,843    140,575    182,549    239,320    297,340    316,594    319,594    397,633    398,634

X(524) = isogonal conjugate of X(111)
X(524) = isotomic conjugate of X(671)
X(524) = complementary conjugate of X(126)
X(524) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,126), (67,141)
X(524) = X(187)-cross conjugate of X(468)
X(524) = crosssum of X(6) and X(187)
X(524) = crossdifference of any two points on line X(6)X(512)
X(524) = X(I)-line conjugate of X(J) for these (I,J): (4,126), (67,141)

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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