## X(1916) (TRILINEAR POLE OF PU(11))

 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) = bc/(a4 - b2c2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1916) lies on these lines:
2,694    4,147    10,257    39,83    76,115    98,385    114,262    226,335    256,291    316,736    325,698    538,671    543,598    690,882    804,881

X(1916) = midpoint of X(148) and X(194)
X(1916) = reflection of X(I) in X(J) for these (I,J): (76,115), (99,39)
X(1916) = isogonal conjugate of X(1691)
X(1916) = isotomic conjugate of X(385)
X(1916) = cevapoint of X(39) and X(511)

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