## X(1687) (INSIMILICENTER(1ST LEMOINE CIRCLE, 2ND LEMOINE 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

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
Trilinears           h(A,B,C) : h(B,C,A): h(C,A,B), where h(A,B,C) = sin(A - ω/2 + π/4)       (M. Iliev, 5/13/07)

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

X(1687) lies on these lines:
3,6    83,2010    98,2009    485,1677    486,1676    1124,1672    1335,1672    1377,1681    1378,1680    1700,1703    1701,1702

X(1687) = reflection of X(1688) in X(1691)
X(1687) = isogonal conjugate of X(2009)
X(1687) = inverse-in-circumcircle of X(1688)
X(1687) = inverse-in-Brocard-circle of X(1690)
X(1687) = inverse-in-1st-Lemoine-circle of X(1688)
X(1687) = X(98)-Ceva conjugate of X(1688)

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