## X(1688) (EXSIMILICENTER(1ST LEMOINE CIRCLE, 2ND LEMOINE CIRCLE))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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) = cos(A - ω) - sin A

Trilinears           g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = cos A - (sec ω - tan ω) sin A

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1688) lies on these lines:
3,6    83,2009    98,2010    485,1676    486,1677    1124,1672    1335,1673    1377,1680    1378,1681    1700,1702    1701,1703

X(1688) = reflection of X(1687) in X(1691)
X(1688) = isogonal conjugate of X(2010)
X(1688) = inverse-in-circumcircle of X(1687)
X(1688) = inverse-in-Brocard-circle of X(1689)
X(1688) = inverse-in-1st-Lemoine-circle of X(1687)
X(1688) = X(98)-Ceva conjugate of X(1687)

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