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

X(1278)
(CONGRUENT MIDWAY-PARALLELIANS POINT)


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) = bc(ab +ac - 3bc)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Antreas Hatzipolakis described this point in Hyacinthos #3190 (7/13/2001). See also

Paul Yiu, Introduction to the Geometry of the Triangle, 2002, Section 3.3.1, exercise 2.

X(1278) lies on these lines: 2,37    8,726    145,740    193,742

X(1278) is the {X(75),X(192)}-harmonic conjugate of X(2). For a list of harmonic conjugates, click More at the top of this page.

X(1278) = reflection of X(192) in X(75)
X(1278) = anticomplement of X(192)

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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