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           a(2a2 - b2 - c2) : b(2b2 - c2 - a2) : c(2c2 - a2 - b2)
                                    =sin A - 3 cos A tan ω : sin B - 3 cos B tan ω : sin C - 3 cos C tan ω (Peter J. C. Moses, 8/22/03)

Barycentrics    a2(2a2 - b2 - c2) : b2(2b2 - c2 - a2) : c2(2c2 - a2 - b2)

X(187) lies on these lines:
2,316    3,6    23,111    30,115    35,172    36,1015    74,248    99,385    110,352    112,186    183,1003    237,351    249,323    325,620    395,531    396,530    729,805

X(187) is the {X(3),X(6)}-harmonic conjugate of X(574).

X(187) is the radical trace of the circumcircle and Brocard circle. (Peter J. C. Moses, 8/24/03)

X(187) = midpoint of X(I) and X(J) for these (I,J): (15,16), (99,385)
X(187) = reflection of X(I) in X(J) for these (I,J): (115,230), (316,625), (325,620)
X(187) = isogonal conjugate of X(671)
X(187) = inverse-in-circumcircle of X(6)
X(187) = inverse-in-Brocard-circle of X(574)
X(187) = complement of X(316)
X(187) = anticomplement of X(625)
X(187) = X(111)-Ceva conjugate of X(6)
X(187) = crosspoint of X(I) and X(J) for these (I,J): (2,67), (6,111), (468,524)
X(187) = crosssum of X(I) and X(J) for these (I,J): (2,524), (6,23), (111,895), (115,690)
X(187) = crossdifference of any two points on line X(2)X(523)
X(187) = X(55)-beth conjugate of X(187)

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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