HJB --- GMA --- UFF


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Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (reasonable trilinears are sought)
Barycentrics    (reasonable barycentrics are sought)

The center X for which the triangle XBC, XCA, XAB have equal Brocard angles. Peter Yff proved that X(368) lies on the self-isogonal conjugate cubic with trilinear equation f(a,b,c)u + f(b,c,a)v + f(c,a,b)w = 0, where f(a,b,c) = bc(b2 - c2) and, for variable x : y : z, the cubics u, v, w are given by u(x,y,z) = x(y2 + z2), v = u(y,z,x), w = u(z,x,y).

Cyril Parry proved that X(368) lies on the anticomplement of the Kiepert hyperbola, this anticomplement being given by the trilinear equation a2(b2 - c2)x2 + b2(c2 - a2)y2 + c2(a2 - b2)z2 = 0.

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.

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Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense

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