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K544

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X(399), X(2931), X(12383)

X(12383) = reflection H' of H about X(110).

A circum-conic with perspector Ω on the orthic axis is a rectangular hyperbola (H) with center G/Ω on the nine points circle and meeting the circumcircle again at the reflection Q of H about G/Ω. The circle with center Q passing through H meets this hyperbola at H and three other points which are the vertices of an equilateral triangle.

The pivotal cubic pK with pole Ω on the orthic axis and with pivot the reflection H' of H about Q is an equilateral pK (a pK60) passing through the vertices of this equilateral triangle.

When Ω = X(3003), (H) contains X(110) and the pK60 is K544 = pK(X3003, X12383) passing through the Parry reflection point X(399).