## X(522) (ISOGONAL CONJUGATE OF X(109))

 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           (cos B - cos C)(csc A) : (cos C - cos A)(csc B) : (cos A - cos B)(csc C)
Barycentrics    cos B - cos C : cos C - cos A : cos A - cos B

As the isogonal conjugate of a point on the circumcircle, X(522) lies on the line at infinity.

X(522) lies on this line: 9,657    30,511    100,655    101,929    190,666    240,656    243,652

X(522) = orthopoint of X(515)
X(522) = isogonal conjugate of X(109)
X(522) = isotomic conjugate of X(664)
X(522) = complementary conjugate of X(124)
X(522) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,124), (8,11), (100,10), (190,9)
X(522) = X(11)-cross conjugate of X(8)
X(522) = crosspoint of X(I) and X(J) for these (I,J): (21,100), (75,190)
X(522) = crosssum of X(I) and X(J) for these (I,J): (6,663), (31,649), (55,652), (65,513), (603,1459), (692,1415)
X(522) = crossdifference of any two points on line X(6)X(41)
X(522) = X(I)-Hirst inverse of X(J) for these (I,J): (514,918), (519,528)

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