## X(631) (3/5*OG)

 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            2 cos A + cos B cos C : 2 cos B + cos C cos A : 2 cos C + cos A cos B
= cos A + sin B sin C : cos B + sin C sin A : cos C + sin A sin B

Barycentrics    (sin A)(2 cos A + cos B cos C) : (sin B)(2 cos B + cos C cos A) : (sin C)(2 cos C + cos A cos B)

X(631) lies on these lines: 1,1000    2,3    10,944    35,497    36,388    54,69    55,1058    56,1056    98,620    104,958    171,602    216,1075    238,601    315,1007    390,496    487,492    488,491    572,966    978,1064

X(631) is the {X(2),X(3)}-harmonic conjugate of X(4).

X(631) = reflection of X(632) in X(140)
X(631) = inverse-in-orthocentroidal-circle of X(3090)
X(631) = complement of X(3091)
X(631) = anticomplement of X(1656)

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