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K501

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X(13), X(14), X(98), X(14356)

other points below

K501 is an equilateral nK0 with pole X(1989), root the barycentric product X(14582) of X(1989) and X(525). See the related cubics K205 and CL054.

The asymptotes bound an equilateral triangle with center X(14639), the intersection of the lines X(4)X(98) and X(5)X(99).

K501 meet the circumcircle at E1, E2 on the perpendicular at X(5) to the Euler line. The third point E3 on this line also lies on the Fermat line X(13)X(14). E3 is X(14356), the X(1989)–isoconjugate of X(98). Recall that X(1989) is the barycentric product of the Fermat points.

The isoconjugates of the infinite points of K501 lie on the circum-conic with perspector X(1989) and eccentricity 2. They form another equilateral with sidelines parallel to the asymptotes of K501.

K501a