## X(628) (ANTICOMPLEMENT OF X(18))

 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) = [SBSC + 2SA(a2 - sqr(3) area)]/a

Trilinears            F(18)/a + 2 sec(A + π/3) : F(18)/b + 2 sec(B + π/3) : F(18)/c + 2 sec(C + π/3)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

Erect equilateral triangles inwards on the sides of triangle ABC; the circumcenter of the apices is X(628). (Peter Moses, 7/16,2003)

X(628) lies on these lines: 2,18    3,299    4,617    5,303    15,636    20,622    54,69    62,619    140,298

X(628) = reflection of X(18) in X(630)
X(628) = anticomplement of X(18)
X(628) = anticomplementary conjugate of X(634)
X(628) = X(303)-Ceva conjugate of X(2)

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