## X(386) (INVERSE-IN-BROCARD-CIRCLE OF X(58))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b2 + c2 + bc + ca + ab)

Trilinears            h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = r cos A + s sin A, s = semiperimeter, r = inradius

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a2(b2 + c2 + bc + ca + ab)

X(386) is the external center of similitude of the circumcircle and Apollonius circle. The internal center is X(573). (Peter J. C. Moses, 8/22/03)

X(386) lies on these lines:
1,2    3,6    31,35    40,1064    55,595    56,181    57,73    65,994    81,404    474,940    758,986    872,984

X(386) is the {X(3),X(6)}-harmonic conjugate of X(58).

X(386) = inverse of X(58) in the Brocard circle
X(386) = crosssum of X(6) in X(1011)
X(386) = crossdifference of any two points on line X(523)X(649)

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