## X(512) (ISOGONAL CONJUGATE OF X(99))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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 , 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           a(b2 - c2) : b(c2 - a2) : c(a2 - b2)
Barycentrics    a2(b2 - c2) : b2(c2 - a2) : c2(a2 - b2)

X(512) is the point in which the line of the 1st and 2nd Brocard points meets the line at infinity.

X(512) lies on these lines: 1,875    4,879    30,511    32,878    39,881    74,842    99,805    110,249    111,843    187,237    316,850    660,1016    670,886

X(512) = orthopoint of X(511)
X(512) = isogonal conjugate of X(99)
X(512) = isotomic conjugate of X(670)
X(512) = anticomplementary conjugate of X(148)
X(512) = complementary conjugate of X(115)

X(512) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,115), (66,125), (99,39), (110,6), (112,32), (1018,1500), (1306,1504), (1307,1505)

X(512) = crosspoint of X(I) and X(J) for these (I,J): (4,112), (6,110), (83,99)

X(512) = crosssum of X(I) and X(J) for these (I,J): (1,1019), (2,523), (3,525), (6,669), (39,512), (100,190), (311,850), (514,1125), (643,662)

X(512) = crossdifference of any two points on line X(2)X(6)
X(512) = X(112)-line conjugate of X(30)

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