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X(2), X(13), X(14), X(67), X(524), X(2770)

points where the orthoptic circle of the Steiner in-ellipse meets the Euler line

K065 = O(X524) is the orthopivotal cubic with orthopivot X(524), the point at infinity of the line X(2)X(6). See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary.

K065 is a central focal cubic with center G. See K1138, another central focal cubic with center G.

The isogonal transform of K065 is the focal cubic K640.