X(526) (ISOGONAL CONJUGATE OF X(476))

 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!

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) = (1 + 2 cos 2A)sin(B - C)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

As the isogonal conjugate of a point on the circumcircle, X(526) lies on the line at infinity.

X(526) lies on these lines: 30,511    67,879    110,351

X(526) = isogonal conjugate of X(476)
X(526) = X(110)-Ceva conjugate of X(1511)
X(526) = crosspoint of X(74) and X(110)
X(526) = crosssum of X(30) and X(523)
X(526) = crossdifference of any two points on line X(6)X(13)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.