## X(237) (X(3)-LINE CONJUGATE OF X(2))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           a2cos(A + ω) : b2cos(B + ω) : c2cos(C + ω)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a3(b4 + c4 - a2b2 - a2c2) (Darij Grinberg, 3/29/03)

Barycentrics    a3cos(A + ω) : b3cos(B + ω) : c3cos(C + ω)

X(237) is the point of intersection of the Euler line and the Lemoine axis (defined as the radical axis of the circumcircle and the Brocard circle).

X(237) lies on these lines: 2,3    6,160    31,904    32,184    39,51    154,682    187,351    206,571

X(237) is the {X(1113),X(1114)}-harmonic conjugate of X(1316).

X(237) = isogonal conjugate of X(290)
X(237) = X(98)-Ceva conjugate of X(6)
X(237) = crosspoint of X(I) and X(J) for these (I,J): (6,98), (232,511)
X(237) = crosssum of X(I) and X(J) for these (I,J): (2,511), (98,287)
X(237) = crossdifference of any two points on line X(2)X(647)
X(237) = X(32)-Hirst inverse of X(184)
X(237) = X(3)-line conjugate of X(2)
X(237) = X(55)-beth conjugate of X(237)

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