## X(3000) ((ANTIORTHIC AXIS)∩(SODDY LINE))

 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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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) = (b + c)a3 + 2(bc - b2 - c2)a2 + (ab + ac - 2bc)(b - c)2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The antiorthic axis is line X(44)X(513), more simply represented as L(1), meaning the line whose coefficients in trilinear coordinates are 1 : 1 : 1, these also being trilinears for X(1). The Soddy line is X(1)X(7), alias L(657). For such identifications as these, use the MathWorld link just before X(3000).

X(3000) lies on these lines:
1,7    241,2310    527,2340

X(3000) = reflection of X(2310) in X(241)
X(3000) = crosssum of X(1) and X(3000)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.