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

X(577)
(HARMONIC OF X(216))


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) = sin A cos2A      (M. Iliev, 4/12/07)
Barycentrics    (sin A)f(A,B,C): (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(577) lies on these lines: 2,95    3,6    20,393    22,232    30,53    48,603    69,248    112,376    141,441    160,206    172,1038    184,418    198,478    219,906    220,268    264,401    395,466    396,465

X(577) = inverse-in-Brocard-circle of X(216)
X(577) = complement of X(317)
X(577) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,184), (9,3)
X(577) = X(418)-cross conjugate of X(3)
X(577) = crosspoint of X(I) and X(J) for these (I,J): (2,68), (3,394)
X(577) = crosssum of X(I) and X(J) for these (I,J): (4,393), (6,24), (324,467)
X(577) = crossdifference of any two points on line X(403)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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