INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(1385)
(MIDPOINT OF INCENTER AND CIRCUMCENTER)


Click here to access the list of all triangle centers.

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 Run Macro Tool, 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) = 16(area ABC)2 + a(a + b + c)(b2 + c2 - a2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1385) lies on these lines:
1,3    2,355    5,515    8,631    10,140    21,104    30,551    37,572    54,72    77,945    78,956    101,1212    182,518    284,1108    376,962    496,950    500,1064    511,1386    516,550    519,549    573,1100    581,995    602,1468    912,960    943,1476    953,1290    958,997    971,1001    991,1279

X(1385) = midpoint of X(I) and X(J) for these (I,J): (1,3), (40,1482), (355,944)
X(1385) = reflection of X(I) in X(J) for these (I,J): (5,1125), (10,140)
X(1385) = isogonal conjugate of X(1389)
X(1385) = complement of X(355)

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



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