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X(6), X(110), X(512), X(3124), X(9218) vertices of the cevian triangle of K Tucker bicevian perspectors (see Bicevian Tucker circles) X = X(3124), K / X(110) = X(9218) 

Any bicevian conic C(P,Q) such that Q = K/P is tangent to the Brocard ellipse. Its center lies on the Brocard axis if and only if P lies on K367 or on K368. In this latter case, the center is always X(39), the Brocard midpoint. The infinite points of K367 are X(512) and two imaginary points, those of the bicevian ellipse C(G,K) or those of the circumellipse C(X39) with perspector X(39) and center X(141). The real asymptote is perpendicular to the Brocard axis and meets the curve at X = X(3124), a point on the line KX(110), on the Brocard ellipse, on C(G,K). K367 is the isogonal transform of pK(X99, X99), a member of the class CL007 : pK(W, W) cubics or parallel tripolars cubics. 
