## X(1723) (MIMOSA TRANSFORM OF X(57))

 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) = - (cos A)/x + (cos B)/y + (cos C)/z,    x : y : z = X(57)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1723) lies on these lines:
1,6    19,46    35,380    36,610    57,1762    90,1172    169,1400    278,1708    281,1737    672,1766    920,1249    928,1047    1707,1709    1718,1783    1722,1880    1729,1744

X(1723) = X(I)-Ceva conjugate of X(J) for these (I,J): (278,1), (1708,46)
X(1723) = crosspoint of X(653) and X(765)
X(1723) = crosssum of X(244) and X(652)
X(1723) = X(I)-aleph conjugate of X(J) for these (I,J): (4,1709), (174,610), (273,1729), (278,1723), (366,1490), (508,1763), (509,1745)

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