## X(1857) (ZOSMA TRANSFORM OF X(223))

 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           (y + z) sec A : (z + x) sec B : (x + y) sec C,    x : y : z = X(223)
Trilinears            [cos(A/2) sec A]2 : [cos(B/2) sec B]2 : [cos(C/2) sec C]2 ( M. Iliev, 4/12/07)
Trilinears            (1 + cos A)/(1 + cos 2A) : (1 + cos B)/(1 + cos 2B) : (1 + cos C)/(1 + cos 2C)      (M. Iliev, 4/12/07)

Barycentrics    (y + z) tan A : (z + x) tan B : (x + y) tan C,    x : y : z = X(223)

X(1857) lies on these lines:
2,243    4,65    8,1896    11,278    33,42    55,281    92,497    189,1364    388,1895    403,1068    412,1788    1478,1784    1748,1776

X(1857) = isogonal conjugate of X(1804)
X(1857) = X(158)-Ceva conjugate of X(393)

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