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

X(381)
(MIDPOINT OF X(2) AND X(4))


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           2 cos(B - C) - cos A : 2 cos(C - A) - cos B : 2 cos(A - B) - cos C
                                 = cos A + 4 cos B cos C : cos B + 4 cos C cos A : cos C + 4 cos A cos B

Barycentrics    a(cos A + 4 cos B cos C) : b(cos B + 4 cos C cos A) : c(cos C + 4 cos A cos B)

X(381) = center of the orthocentroidal circle

X(381) lies on these lines:
2,3    6,13    11,999    49,578    51,568    54,156    98,598    114,543    118,544    119,528    125,541    127,133    155,195    183,316    184,567    210,517    262,671    264,339    298,622    299,621    302,616    303,617    355,519    388,496    495,497    511,599    515,551

X(381) is the {X(4),X(5)}-harmonic conjugate of X(3) and also the {X(13),X(14)}-harmonic conjugate of X(6).

X(381) = midpoint of X(2) and X(4)
X(381) = reflection of X(I) in X(J) for these (I,J): (2,5), (3,2), (376,549), (549,547), (568,51)
X(381) = complement of X(376)
X(381) = anticomplement of X(549)
X(381) = crossdifference of any two points on line X(526)X(647)

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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