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

X(376)
(CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2))


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.

The JRE (Java Runtime Environment) is not enabled in your browser!

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           5 cos A - cos(B - C) : 5 cos B - cos(C - A) : 5 cos C - cos(A - B)
                               = 2 cos A - cos B cos C : 2 cos B - cos C cos A : 2 cos C - cos A cos B
                                 = f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (csc A)(5 sin 2A - sin 2B - sin 2C)

Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 5 sin 2A - sin 2B - sin 2C

X(376) is the reflection of X(2) in X(3).

X(376) lies on these lines:
1,553    2,3    35,388    36,497    40,519    55,1056    56,1058    69,74    98,543    103,544    104,528    110,541    112,577    165,515    316,1007    390,999    476,841    477,691    487,490    488,489    516,551

X(376) is the {X(3),X(20)}-harmonic conjugate of X(4).

X(376) = midpoint of X(2) and X(20)
X(376) = reflection of X(I) in X(J) for these (I,J): (2,3), (4,2), (381,549)
X(376) = anticomplement of X(381)

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



free counter