## X(1742) (MIMOSA TRANSFORM OF X(212))

 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(212)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1742) lies on these lines:
1,7    3,238    35,1745    40,511    43,165    48,1633    87,572    259,503    266,844    376,1064    651,1253    846,1709    971,984

X(1742) = reflection of X(1) in X(991)
X(1742) = X(55)-Ceva conjugate of X(1)
X(1742) = X(I)-aleph conjugate of X(J) for these (I,J): (1,57), (6,978), (9,40), (55,1742), (174,1445), (188,63), (259,1), (365,1743), (366,169)

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