## X(1706) (EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE))

 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) = bc[2(b + c) - a(cos A - cos B - cos C + 1)]
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a3 + a2(b + c) - a(b + c)2 - (b + c)(b2 - 6bc + c2)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The insimilicenter of the Bevan and Spieker circles is X(9).

X(1706) lies on these lines:
1,474    2,1697    4,9    8,57    46,529    65,200    84,355    165,958    404,1420    517,936    1329,1699    1377,1702    1378,1703    1571,1573    1572,1574    1678,1704    1679,1705    1680,1700    1681,1701

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