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

X(651)
(TRILINEAR POLE OF LINE X(1)X(3))


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            1/(cos B - cos C) : 1/(cos C - cos A) : 1/(cos A - cos B)
                                    = 1/[(b - c)(b + c - a)] : 1/[(c - a)(c + a - b)] : 1[(a - b)(a + b - c)]
Barycentrics    (sin A)/(cos B - cos C) : (sin B)/(cos C - cos A) : (sin C)/(cos A - cos B)
                                    = a/[(b - c)(b + c - a)] : b/[(c - a)(c + a - b)] : c/[(a - b)(a + b - c)]

X(651) lies on these lines:
2,222    6,7    8,221    9,77    21,73    44,241    57,88    59,513    63,223    65,895    69,478    81,226    100,109    101,934    108,110    144,219    155,1068    190,644    193,608    218,279    255,411    287,894    329,394    404,603    500,943    514,655    645,799    648,823    978,1106

X(651) = isogonal conjugate of X(650)
X(651) = cevapoint of X(101) and X(109)
X(651) = X(I)-cross conjugate of X(J) for these (I,J): (6,59), (101,100), (513,7), (514,81), (521,77)
X(651) = crosssum of X(I) and X(J) for these (I,J): (647,661), (657,663)

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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