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

X(141)
(COMPLEMENT OF SYMMEDIAN POINT)


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           bc(b2 + c2) : ca(c2 + a2) : ab(a2 + b2)
                                    = csc2A sin(A + ω) : csc2B sin(B + ω) : csc2C sin(C + ω)

Barycentrics    b2 + c2 : c2 + a2 : a2 + b2

X(141) = X(6)-of-medial triangle

X(141) lies on these lines:
2,6    3,66    5,211    10,142    37,742    39,732    45,344    53,264    67,110    75,334    76,698    95,287    99,755    113,127    116,121    125,126    140,182    239,319    241,307    308,670    311,338    317,458    320,894    384,1031    441,577    498,611    499,613    523,882    542,549    575,629    997,1060

X(141) is the {X(2),X(69)}-harmonic conjugate of X(6).

X(141) = midpoint of X(I) and X(J) for these (I,J): (6,69), (66,159), (67,110)
X(141) = reflection of X(I) in X(J) for these (I,J): (182,140), (597,2), (1353,575), (1386,1125)
X(141) = isogonal conjugate of X(251)
X(141) = isotomic conjugate of X(83)
X(141) = inverse-in-nine-point-circle of X(625)
X(141) = complement of X(6)
X(141) = complementary conjugate of X(2)
X(141) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,39), (67,524), (110,525)
X(141) = X(39)-cross conjugate of X(427)
X(141) = crosspoint of X(2) and X(76)
X(141) = crosssum of X(6) and X(32)
X(141) = X(39)-Hirst inverse of X(732)
X(141) = X(645)-beth conjugate of X(141)


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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