## X(664) (TRILINEAR POLE OF LINE X(2)X(7))

 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.

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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            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a(b - c)(b + c - a)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(664) lies on these lines:
1,85    7,528    8,348    69,347    73,290    75,77    99,109    100,658    101,514    145,279    150,952    175,490    176,489    190,644    223,312    226,671    239,241    307,319    322,326    648,653    668,1026    1018,1025

X(664) = reflection of X(1121) in X(2)
X(664) = isogonal conjugate of X(663)
X(664) = isotomic conjugate of X(522)
X(664) = X(I)-cross conjugate of X(J) for these (I,J): (100,190), (514,85), (521,333), (522,2)
X(664) = crosssum of X(512) and X(810)

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