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

X(3234)
(VERTEX OF THE INSCRIBED YFF PARABOLA)


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(2a3 - b3 - c3 - a2b - a2c + b2c + bc2)2/(b - c)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3234) lies on these lines: 101,514    118,516    1633,2736

Propetries of the inscribed Yff parabola: center = X(514); perspector = X(190), focus = X(101); directrix = X(4)X(9), the trilinear pole of X(1897). The parabola passes through these points: X(514), X(649), X(3234), X(3239). The axis of the parabola is X(101)X(514), and the Simson line of the focus is X(118)X(516). Contributed by Peter Moses, April 6, 2007.

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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