## X(520) (ISOGONAL CONJUGATE OF X(107))

 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 , 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           (cos A)(sin 2B - sin 2C) : (cos B)(sin 2C - sin 2A) : (cos C)(sin 2A - sin 2B)
Barycentrics    (sin 2A)(sin 2B - sin 2C) : (sin 2B)(sin 2C - sin 2A) : (sin 2C)(sin 2A - sin 2B)

As the isogonal conjugate of a point on the circumcircle, X(520) lies on the line at infinity.

X(520) lies on these lines: 30,511    69,879    110,250    340,850    647,652

X(520) = isogonal conjugate of X(107)
X(520) = complementary conjugate of X(122)
X(520) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,122), (68,125), (110,3)
X(520) = crosspoint of X(3) and X(110)
X(520) = crosssum of X(I) and X(J) for these (I,J): (4,523), (51,647), (512,800)
X(520) = crossdifference of any two points on line X(4)X(6)

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