## X(1990) (ORTHIC-AXIS INTERCEPT OF LINE X(4)X(6))

 Interactive Applet

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 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) = bc[a2(b2 + c2 - 2a2) + (b2 - c2)2]/(b2 + c2 - a2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = [a2(b2 + c2 - 2a2) + (b2 - c2)2]/(b2 + c2 - a2)

X(1990) is described in section 6.4.2 of the downloadable article cited at X(1989).

X(1990) lies on these lines:
4,6    44,1785    50,112    140,216    186,1138    230,231    297,340    395,471    396,470    403,1989    458,597    550,577    1033,1609

X(1990 = midpoint of X(297) and X(648)
X(1990) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,133), (1300,25), (1989,53)
X(1990) = crosspoint of X(2) and X(1294)

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