## X(517) (ISOGONAL CONJUGATE OF X(104))

 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           -1 + cos B + cos C : -1 + cos C + cos A : -1 + cos A + cos B
Barycentrics    (sin A)(-1 + cos B + cos C) : (sin B)(-1 + cos C + cos A) : (sin C)(-1 + cos A + cos B)

As the isogonal conjugate of a point on the circumcircle, X(517) lies on the line at infinity.

X(517) lies on these lines:
1,3    2,392    4,8    5,10    6,998    7,1000    9,374    19,219    20,145    30,511    37,573    42,1064    63,956    78,945    100,953    101,910    104,901    119,908    169,220    210,381    226,495    238,1052    389,950    549,551    572,1100    580,595    582,602    938,1058    1042,1066

X(517) = orthopoint of X(513)
X(517) = isogonal conjugate of X(104)
X(517) = anticomplementary conjugate of X(153)
X(517) = complementary conjugate of X(119)
X(517) = X(4)-Ceva conjugate of X(119)
X(517) = crosspoint of X(I) and X(J) for these (I,J): (1,80), (7,88)
X(517) = crosssum of X(I) and X(J) for these (I,J): (1,36), (3,912), (44,55), (56,1455)
X(517) = crossdifference of any two points on line X(6)X(650)

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