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

X(1086)
(CENTER OF HYPERBOLA {A,B,C,X(2),X(7)})


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) = bc(b - c)2
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b - c)2

The line f(a,b,c)x + f(b,c,a)y + f(c,a,b)z = 0 is tangent to the circumcircle at X(101). Also, X(1086) is the point of tangency of the Steiner inscribed ellipse with the line tangent to the nine-point circle and the incircle. (Paul Yiu, #4197, 11/24/01).

X(1086) lies on these lines:
1,528    2,45    6,7    8,599    10,537    11,244    37,142    44,527    53,273    57,1020    75,141    115,116    220,277    239,320    812,1015    918,1111

X(1086) = midpoint of X(I) and X(J) for these (I,J): (2,903), (7,673), (75,335), (239,320)
X(1086) = isogonal conjugate of X(1252)
X(1086) = isotomic conjugate of X(1016)
X(1086) = complement of X(190)
X(1086) = crosspoint of X(2) and X(514)
X(1086) = crosssum of X(I) and X(J) for these (I,J): (6,101), (9,1018), (32,692), (219,906)
X(1086) = crossdifference of any two points on line X(101)X(692)

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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