## X(1122) (1ST GRINBERG POINT)

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

Let Ab be the touchpoint of the A-excircle and line AB, let Ac be the touchpoint of the A-excircle and line AC, and let Ma be the midpoint of segment AbAc. Define Mb and Mc cyclically. Let A', B', C' be the touchpoints of the incircle with lines BC, CA, AB, respectively. The triangles MaMbMc and A'B'C' are perspective, and the perspector is X(1122). (Darij Grinberg, 12/28/02)

X(1122) lies on these lines: 7,8    56,269

X(1122) = isogonal conjugate of X(1261)
X(1122) = crosspoint of X(7) and X(269)
X(1122) = crosssum of X(55) and X(200)

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