X(38) (CROSSPOINT OF X(1) AND X(75))

 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 , 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           b2 + c2 : c2 + a2 : a2 + b2
=csc A sin(A + ω) : csc B sin(B + ω) : csc C sin(C + ω)

Barycentrics    a(b2 + c2) : b(c2 + a2) : c(a2 + b2)
= sin(A + ω) : sin(B + ω) : sin(C + ω)

X(38) lies on these lines:
1,21    2,244    3,976    8,986    9,614    10,596    37,354    42,518    56,201    57,612    75,310    78,988    92,240    99,745    210,899    321,726    869,980    912,1064    1038,1106

X(38) is the {X(1),X(63)}-harmonic conjugate of X(31).

X(38) = isogonal conjugate of X(82)
X(38) = isotomic conjugate of X(3112)
X(38) = anticomplement of X(1215)
X(38) = crosspoint of X(1) and X(75)
X(38) = crosssum of X(1) and X(31)
X(38) = crossdifference of any two points on line X(661)X(830)
X(38) = X(643)-beth conjugate of X(38)

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