## X(946) (MIDPOINT OF X(1) AND X(4))

 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            f(a,b,c) : f(b,c,a) : f(c,a,b),
where f(a,b,c) = bc[a3(b + c) + (b - c)2(a2 - ab - ac - b2 - c2 - 2bc)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(946) lies on these lines:
1,4    2,40    3,142    5,10    7,84    8,908    11,65    29,102    30,551    46,499    56,1012    79,104    165,631    238,580    355,381    392,442    496,942    546,952    951,1067

X(946) = midpoint of X(I) and X(J) for these (I,J): (1,4), (40,962)
X(946) = reflection of X(I) in X(J) for these (I,J): (3,1125), (10,5)
X(946) = inverse-in-incircle of X(1785)
X(946) = isogonal conjugate of X(947)
X(946) = complement of X(40)
X(946) = crosspoint of X(I) and X(J) for these (I,J): (2,309), (7,92)
X(946) = crosssum of X(48) and X(55)

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