## X(1909) (CROSSSUM OF PU(9))

 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 + bc/a2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1909) lies on these lines:
1,76    2,330    7,8    10,274    12,325    34,264    35,99    36,1078    37,1655    42,310    56,183    73,290    86,313    172,385    190,1334    226,1432    256,1221    257,335    286,1891    305,612    315,1478    538,1500    732,894    1215,1237    1235,1870

X(1909) = isogonal conjugate of X(904)
X(1909) = isotomic conjugate of X(256)
X(1909) = anticomplement of X(1107)
X(1909) = X(I)-Ceva conjugate of X(J) for these (I,J): (335,350), (1221,2)
X(1909) = cevapoint of X(8) and X(1655)

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