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

X(237)
(X(3)-LINE CONJUGATE OF X(2))


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           a2cos(A + ω) : b2cos(B + ω) : c2cos(C + ω)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a3(b4 + c4 - a2b2 - a2c2) (Darij Grinberg, 3/29/03)

Barycentrics    a3cos(A + ω) : b3cos(B + ω) : c3cos(C + ω)

X(237) is the point of intersection of the Euler line and the Lemoine axis (defined as the radical axis of the circumcircle and the Brocard circle).

X(237) lies on these lines: 2,3    6,160    31,904    32,184    39,51    154,682    187,351    206,571

X(237) is the {X(1113),X(1114)}-harmonic conjugate of X(1316).

X(237) = isogonal conjugate of X(290)
X(237) = X(98)-Ceva conjugate of X(6)
X(237) = crosspoint of X(I) and X(J) for these (I,J): (6,98), (232,511)
X(237) = crosssum of X(I) and X(J) for these (I,J): (2,511), (98,287)
X(237) = crossdifference of any two points on line X(2)X(647)
X(237) = X(32)-Hirst inverse of X(184)
X(237) = X(3)-line conjugate of X(2)
X(237) = X(55)-beth conjugate of X(237)

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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