## X(3031) (INTERSECTION X(10)X(125)∩X(74)X(573))

 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) = a(b + c)2(a3 + b3 - c3 + a2c - b2c - ac2)(a3 - b3 + c3 + a2b - bc2 - ab2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3031) lies on the Apollonius circle and these lines:
10,125    43,2948    74,573    110,386    113,2051    690,3029    1017,2092    2774,3033    2836,3034    2842,3030

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