## X(213) (X(6)-CEVA CONJUGATE OF X(42))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (b + c)a2 : (c + a)b2 : (a + b)c2
Barycentrics    (b + c)a3 : (c + a)b3 : (a + b)c3

X(213) lies on these lines: 1,6    8,981    31,32    39,672    58,101    63,980    83,239    100,729    184,205    274,894    607,1096    667,875    692,923

X(213) = isogonal conjugate of X(274)
X(213) = X(I)-Ceva conjugate of X(J) for these (I,J): (6,42), (37,228)
X(213) = crosspoint of X(6) and X(31)
X(213) = crosssum of X(I) and X(J) for these (I,J): (2,75), (81,1444), (85,348)
X(213) = crossdifference of any two points on line X(320)X(350)
X(213) = X(I)-beth conjugate of X(J) for these (I,J): (41,213), (101,65), (644,213)

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

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Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense