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

X(2078)
(INVERSE-IN-CIRCUMCIRCLE OF X(57))


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) = r - 2R + 2(r + R) cos A
                                    = g(A,B,C) : g(B,C,A) : g(C,A,B),
                                    where g(A,B,C) = cos B + cos C - 3 + (1 + 2 cos A + 2 cos B + 2 cos C) cos A
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a(a2 + b2 + c2 - 2ab - 2ac + bc)/(b+c-a)       (M. Iliev, 5/13/07)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2078) lies on these lines:
1,3    31,2003    59,672    73,595    105,2006    109,840    226,1005    388,535    581,1497    901,1477    1174,1202    1279,1421    1283,1284    1308,1323

X(2078) = inverse-in-circumcircle of X(57)
X(2078) = crosssum of X(142) and X(527)

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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