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

X(3005)
((DE LONGCHAMPS LINE)∩(LEMOINE AXIS))


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) = a(b4 - c4)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3005) lies on these lines:
2,881    237,351    325,523    661,756    689,783    826,2474    878,2623

X(3005) = reflection of X(I) in X(J) for these I,J: 669,647    2528,2525
X(3005) = isotomic conjugate of X(689)
X(3005) = X(I)-Ceva conjugate of X(J) for these I,J: 512,688    523,826    827,6    1634,39
X(3005) = X(2531)-cross conjugate of X(688)
X(3005) = crosspoint of X(I) and X(J) for these I,J: 6,827    39,1634    512,523
X(3005) = crosssum of X(I) and X(J) for these I,J: 2,826    99,110    512,1194

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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