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

X(3102)
(INNER VERTEX OF THE BROCARD SQUARE)


Click here to access the list of all triangle centers.

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 cos2A - a2cos B cos C + ab sin B + ac sin C
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The 1st Brocard point (trilinears c/b : a/c : b/a) and 2nd Brocard point (b/c : c/a : a/b) are opposing vertices of a square here called the Brocard square. The other two vertices are X(3102) and X(3103). Both are on the Brocard axis X(3)X(6), and X(3102) is the closer to X(3).

X(3102) lies on these lines:
3,6    76,486    194,488    262,485    325,640    2782,3071

X(3102) = reflection of X(3103) in X(39)

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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