HJB --- GMA --- UFF


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: (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) = (cos A)[cos2B + cos2C - cos2A]
Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)

X(4) of the tangential triangle. This point is also the center of the circle which cuts (extended) lines BC, CA, AB in pairs of points A' and A", B' and B", C' and C", respectively, such that angles A'AA", B'BB", C'CC" are all right angles. This is the Dou circle, described in

Jordi Dou, Problem 1140, Crux Mathematicorum, 28 (2002) 461-462.

X(155) lies on these lines:

1,90    3,49    4,254    5,6    20,323    24,110    25,52    26,154    30,1498    159,511    195,381    382,399    450,1075    648,1093    651,1068

X(155) is the {X(26),X(156)}-harmonic conjugate of X(154). For a list of harmonic conjugates of X(155), click More at the top of this page.

X(155) = reflection of X(I) in X(J) for these (I,J): (3,1147), (26,156), (68,5)
X(155) = isogonal conjugate of X(254)
X(155) = eigencenter of cevian triangle of X(4)
X(155) = eigencenter of anticevian triangle of X(3)
X(155) = X(4)-Ceva conjugate of X(3)
X(155) = crosssum of X(136) and X(523)

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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