## X(372) ({X(3),X(6)}-HARMONIC CONJUGATE OF X(371))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           cos(A + π/4) : cos(B + π/4) : cos(C + π/4)
= cos A - sin A : cos B - sin B : cos C - sin C

Barycentrics    sin A cos(A + π/4) : sin B cos(B + π/4) : sin C cos(C + π/4)

X(372) is the external center of similitude of the circumcircle and the 2nd Lemoine circle (cosine circle) (Peter J. C. Moses, 5/9/03). Also, X(372) is the external center of similitude of the Gallatly circle (defined just before X(2007)) and the 1st Lemoine circle (Peter J. C. Moses, 9/10/03).

For details and references, see X(371).

X(372) lies on these lines:
2,485    3,6    4,486    25,494    193,487    315,492    601,605    602,606

X(372) = reflection of X(I) in X(J) for these (I,J): (315,639), (371,32), (638,640)
X(372) = isogonal conjugate of X(486)
X(372) = inverse-in-Brocard-circle of X(371)
X(372) = inverse-in-1st-Lemoine-circle of X(2462)
X(372) = complement of X(638)
X(372) = anticomplement of X(640)
X(372) = X(4)-Ceva conjugate of X(371)

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