## X(521) (ISOGONAL CONJUGATE OF X(108))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (sec B - sec C)(csc A) : (sec C - sec A)(csc B) : (sec A - sec B)(csc C)
Barycentrics    sec B - sec C : sec C - sec A : sec A - sec B

As the isogonal conjugate of a point on the circumcircle, X(521) lies on the line at infinity.

X(521) lies on these lines: 30,511    59,100    650,1021    656,810

X(521) = isogonal conjugate of X(108)
X(521) = complementary conjugate of X(123)
X(521) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,123), (100,3)
X(521) = crosspoint of X(8) and X(100)
X(521) = crosssum of X(I) and X(J) for these (I,J): (33,650), (56,513), (429,523), (663,1400)
X(521) = crossdifference of any two points on line X(6)X(19)

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