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K408

X(2), X(4235), X(14977)

X(4235) = (b^2+c^2-2a^2) / [(b^2-c^2)SA] : : , on the Euler line

X(14977) = isotomic conjugate of X(4235) = (b^2-c^2)SA / (b^2+c^2-2a^2) : : , on the perpendicular at G to the Euler line

K408 is a member of the class CL046.

Let (C) be a circum-conic through G = X(2) and (N) its normal at G. (N) meets (C) at G and another point M which lies on K408.

K408 is an isotomic cK with singularity G and root X(1992), the orthocorrespondent of G. It is the reflection of X(I) in X(J) for these (I,J): (2,6), (69,2), (599, 597)
 and also the anticomplement of X(599).

The pivotal conic is the Lemoine ellipse of the antimedial triangle. Its center is X(599) and its real foci are G and X(69).

Since G lies on Q003, the trilinear polar (L2) of the root X(1992) is parallel to the line (L1) which contains the three real inflexion points. (L1) is the image of (L2) under the homothety h(G, 4).