## X(1745) (MIMOSA TRANSFORM OF X(255))

 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) = sec B + sec C - sec A     (D. Grinberg, 2/25/04)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1745) lies on these lines:
1,4    35,1742    36,978    43,46    78,1330    255,411    579,610    908,1076    920,1758    1464,1836    1716,1756

X(1745) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,1), (1935,1046)
X(1745) = X(1148)-cross conjugate of X(1)
X(1745) = X(I)-aleph conjugate of X(J) for these (I,J): (1,46), (2,1726), (3,1745), (6,1716), (63,1763), (174,1708), (188,1158), (259,1721), (266,1722), (365,1707), (366,19), (508,1729), (509,1723), (651,1020)

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