## X(325) (X(2)-HIRST INVERSE OF X(69))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           csc2A cos(A + ω) : csc2B cos(B + ω) : csc2C cos(C + ω)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(b4 + c4 - a2b2 - a2c2)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b4 + c4 - a2b2 - a2c2

X(325) lies on these lines:
2,6    3,315    5,76    11,350    22,160    25,317    30,99    39,626    114,511    115,538    187,620    232,297    250,340    264,305    274,442    383,622    523,684    621,1080

X(325) = midpoint of X(I) and X(J) for these (I,J): (99,316), (298,299)
X(325) = reflection of X(I) in X(J) for these (I,J): (115,625), (187,620), (385,230), (1513,114)
X(325) = isogonal conjugate of X(1976)
X(325) = complement of X(385)
X(325) = anticomplement of X(230)
X(325) = cevapoint of X(2) and X(147)
X(325) = X(I)-cross conjugate of X(J) for these (I,J): (114,2), (511,297)
X(325) = crossdifference of any two points on line X(32)X(512)
X(325) = X(2)-Hirst inverse of X(69)

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