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X(1), X(5), X(54), X(110), X(523), X(1113), X(1114), X(2574), X(2575)

K316 is an isogonal pivotal cubic with pivot X(110) on the circumcircle. See Table 17.

It has three real asymptotes :

• one is the line perpendicular at X(5) to the Euler line i.e. the perpendicular bisector of OH,

• the others are parallel to the asymptotes of the Jerabek hyperbola and meet at X(1511) midpoint of OX(110).

The isopivot being X(523), the tangents at A, B, C, X(110) are all perpendicular to the Euler line.

K316 meets the Fermat line at three points which also lie on Q003, the Euler-Morley quintic. Consequently, K316 meets the Euler-Morley quartic Q002 at A, B, C, the in/excenters, X(2574), X(2575) and three other points that lie on the isogonal transform of the Fermat line which is the circum-conic passing through X(15), X(16) and also X(2), X(186), X(249), X(323), X(842), X(1138), X(2411).

K316's sister is K839 as in Table 58.