X(518) (ISOGONAL CONJUGATE OF X(105))

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

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           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = ab + ac - b2 - c2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

As the isogonal conjugate of a point on the circumcircle, X(518) lies on the line at infinity.

X(518) lies on these lines:
1,6    2,210    7,8    10,141    11,908    30,511    38,42    43,982    55,63    56,78    57,200    59,765    144,145    209,306    239,335    244,899    329,497    551,597    583,1009    612,940    896,902    997,999

X(518) = isogonal conjugate of X(105)
X(518) = complementary conjugate of X(120)
X(518) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,120), (335,37)
X(518) = crosspoint of X(1) and X(291)
X(518) = crosssum of X(I) and X(J) for these (I,J): (1,238), (56,1456)
X(518) = crossdifference of any two points on line X(6)X(513)
X(518) = X(I)-Hirst inverse of X(J) for these (I,J): (1,9), (6,1083)
X(518) = X(I)-line conjugate of X(J) for these (I,J): (1,6), (30,513)

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