X(187) (INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           a(2a2 - b2 - c2) : b(2b2 - c2 - a2) : c(2c2 - a2 - b2)
=sin A - 3 cos A tan ω : sin B - 3 cos B tan ω : sin C - 3 cos C tan ω (Peter J. C. Moses, 8/22/03)

Barycentrics    a2(2a2 - b2 - c2) : b2(2b2 - c2 - a2) : c2(2c2 - a2 - b2)

X(187) lies on these lines:
2,316    3,6    23,111    30,115    35,172    36,1015    74,248    99,385    110,352    112,186    183,1003    237,351    249,323    325,620    395,531    396,530    729,805

X(187) is the {X(3),X(6)}-harmonic conjugate of X(574).

X(187) is the radical trace of the circumcircle and Brocard circle. (Peter J. C. Moses, 8/24/03)

X(187) = midpoint of X(I) and X(J) for these (I,J): (15,16), (99,385)
X(187) = reflection of X(I) in X(J) for these (I,J): (115,230), (316,625), (325,620)
X(187) = isogonal conjugate of X(671)
X(187) = inverse-in-circumcircle of X(6)
X(187) = inverse-in-Brocard-circle of X(574)
X(187) = complement of X(316)
X(187) = anticomplement of X(625)
X(187) = X(111)-Ceva conjugate of X(6)
X(187) = crosspoint of X(I) and X(J) for these (I,J): (2,67), (6,111), (468,524)
X(187) = crosssum of X(I) and X(J) for these (I,J): (2,524), (6,23), (111,895), (115,690)
X(187) = crossdifference of any two points on line X(2)X(523)
X(187) = X(55)-beth conjugate of X(187)

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