## X(1757) (MIMOSA TRANSFORM OF X(295))

 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) = (b + c)2 - (a + b)(a + c)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1757) lies on these lines:
1,6    10,894    42,846    43,63    57,1463    81,756    100,896    171,210    190,740    191,1045    200,1707    209,1762    239,726    240,1783    314,1089    320,1698    333,1215    484,513    527,1738    672,1282    765,1110    899,1054

X(1757) = reflection of X(I) in X(J) for these (I,J): (1,238), (238,44)
X(1757) = isogonal conjugate of X(1929)
X(1757) = X(291)-Ceva conjugate of X(1)
X(1757) = crosspoint of X(660) and X(765)
X(1757) = crosssum of X(I) and X(J) for these (I,J): (244,659), (1931,1963)
X(1757) = X(I)-aleph conjugate of X(J) for these (I,J): (291,1757), (660,1026)

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