## X(858) (COMPLEMENT OF X(23))

 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) = sin3C sin 2B sin(C - A) + sin3B sin 2C sin(B - A)
Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)

X(858) lies on these lines: 2,3    50,230    67,524    125,511    126,625    316,691    325,523    842,925

X(858) = midpoint of X(316) and X(691)
X(858) = reflection of X(23) in X(468)
X(858) = isogonal conjugate of X(1177)
X(858) = inverse-in-circumcircle of X(22)
X(858) = inverse-in-nine-point-circle of X(2)
X(858) = inverse-in-orthocentroidal-circle of X(1995) X(858) = complement of X(23)
X(858) = anticomplement of X(468)
X(858) = crosssum of X(184) and X(187)
X(858) = crossdifference of any two points on line X(32)X(647)

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