## X(1999) (ORTHOCORRESPONDENT OF X(10))

 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) = yz + (-x cos A + y cos B + z cos C)x, where x : y : z = X(10)
Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(a3 + a2b + a2c + abc - b2c - bc2)       (M. Iliev, 5/13/07)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1999) lies on these lines:
1,2    6,312    27,295    37,333    63,192    75,940    81,314    100,1402    171,740    193,329    226,1943    319,1211    350,1965    553,1266    664,1427

X(1999) = X(65)-Ceva conjugate of X(894)

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