## X(851) (X(65)-HIRST INVERSE OF X(73))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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Download all construction files and macros: tc.zip (10.1 Mb).
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) = sin 2B sin(C - A) + sin 2C sin(B - A)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (cos A + cos B + cos C) csc A - (csc A + csc B + csc C) cos A

Barycentrics    h(A,B,C) : h(B,C,A) : h(C,A,B), where h(A,B,C) = (sin A)f(A,B,C)

X(851) lies on these lines: 2,3    42,65    43,46    44,513    226,228

X(851) = reflection of X(855) in X(859)
X(851) = inverse-in-orthocentroidal-circle of X(1985)
X(851) = crosssum of X(1) and X(851)
X(851) = crossdifference of any two points on line X(1)X(647)
X(851) = X(65)-Hirst inverse of X(73)

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

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Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense