## X(846) (4th SHARYGIN POINT)

 Interactive Applet

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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) = - a2 + b2 + c2 + bc + ca + ab
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a f(a,b,c)

This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #3001, June 11, 2001. For the construction as a Sharygin point, see the description at X(1281).

X(846) lies on these lines: 1,21    2,1054    6,1051    9,43    35,228    37,171    55,984    100,756    333,740    405,986    982,1001

X(846) = X(I)-Ceva conjugate of X(J) for these (I,J): (37,1), (171,43)

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