## X(186) (INVERSE-IN-CIRCUMCIRCLE OF X(4))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           4 cos A - sec A : 4 cos B - sec B : 4 cos C - sec C
= sin 3A csc 2A : sin 3B csc 2B : sin 3C csc 2C

Barycentrics    (sin A)(4 cos A - sec A) : (sin B)(4 cos B - sec B) : (sin C)(4 cos C - sec C)

X(186) lies on these lines: 2,3    54,389    93,252    98,935    107,477    112,187    249,250

X(186) is the {X(3),X(24)}-harmonic conjugate of X(4).

X(186) = reflection of X(I) in X(J) for these (I,J): (4,403), (403,468)
X(186) = isogonal conjugate of X(265)
X(186) = isotomic conjugate of X(328)
X(186) = complement of X(3153)
X(186) = anticomplement of X(2072)
X(186) = inverse-in-circumcircle of X(4)
X(186) = X(340)-Ceva conjugate of X(323)
X(186) = X(50)-cross conjugate of X(323)
X(186) = crosspoint of X(54) and X(74)
X(186) = crosssum of X(I) and X(J) for these (I,J): (5,30), (621,622)
X(186) = crossdifference of any two points on line X(216)X(647)

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