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X(1), X(2), X(5), X(6), X(395), X(396), X(523), X(5000), X(5001), X(5723)

excenters

infinite points of K002

other points below

Let N be the orthocenter of the anticevian triangle of M.

The line MN passes through a fixed point P if and only if M lies on a circum-quartic Q(P) which passes through the in/excenters and P.

When P lies on the Euler line, Q(P) also passes through X(2), X(5000), X(5001) and six other fixed points on the sidelines of the medial triangle. Three of these points lie on the trilinear polar of X(7) and three are the midpoints of the internal bisectors. Their barycentrics are {b ± c, b, ±c}, {a, a ± c, ±c}, {a, ±b, a ± b}.

With P = X(3), X(20), X(5) we obtain the quartics Q026, Q115, Q195 respectively.