## X(1682) (INSIMILICENTER(INCIRCLE, APOLLONIUS 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) = [s cos(A/2) - r sin(A/2)]2
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a(b + c - a)(b2 + c2 + ab + ac)2       (M. Iliev, 5/13/07)

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

The exsimilicenter of the incircle and Apollonius circle is X(181). Also, the triangle A'B'C' formed (as at X(2092) by the intersections of the Apollonius circle and the excircles is perspective to the cevian triangle of X(1), and the perspector is X(1682). (Paul Yiu, Hyacinthos #8076, 10/01/03)

X(1682) lies on these lines: 1,181    3,1397    10,11    43,1697    55,386    56,573    57,1695    73,1362    212,1472    215,501    988,1401    1124,1686    1335,1685    1672,1684    1673,1683    1674,1694    1675,1693    2007,2020    2008,2019

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