## X(2975) (INSIMILICENTER(CIRCUMCIRCLE, AC-INCIRCLE)

 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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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            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a3 + a(bc - b2 - c2) - bc(b + c)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The term "AC-incircle" is introduced for "anticomplement of the incircle" by Peter Moses (Dec. 2, 2004). Thus, the AC-incircle is the incircle of the anticomplementary triangle; the circle has center X(8) and radius 2r. The exsimilicenter of the circumcircle and AC-incircle is X(100), their touchpoint, and the anticomplement of X(11).

X(2975) = anticomplement of X(12)
X(2975) = X(I)-Ceva conjugate of X(J) for these I,J: 59,100    261,2
X(2975) = crosssum of X(512) and X(2170)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

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