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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.
|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)