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

X(1656)
(INTERSECTION OF EULER LINE AND LINE X(17)X(18))


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) = 3 cos A + 4 cos B cos C
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1656) lies on these lines:
2,3    6,17    10,1482    11,498    12,499    49,569    51,1216    125,399    141,1351    302,634    303,633    355,1125    373,568    485,615    486,590    517,1698    567,1147    576,599

X(1656) = midpoint of X(5) and X(632)
X(1656) = reflection of X(I) in X(J) for these (I,J): (3,631), (631,632)
X(1656) = inverse-in-orthocentroidal-circle of X(140)
X(1656) = complement of X(631)
X(1656) = anticomplement of X(632)

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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