## X(670) (TRILINEAR POLE OF LINE X(2)X(39))

 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/[a3(b2 - c2)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(670) lies on these lines:
2,1084    69,290    76,338    99,804    110,689    141,308    190,799    310,903    512,886    645,666    850,892

X(670) = reflection of X(694) in X(141)
X(670) = isogonal conjugate of X(669)
X(670) = isotomic conjugate of X(512)
X(670) = anticomplement of X(1084)
X(670) = X(I)-cross conjugate of X(J) for these (I,J): (512,2), (523,308)
X(670) = crossdifference of any two points on line X(887)X(1084)

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