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K1138

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X(2), X(13), X(14), X(30), X(476), X(5463), X(5464), X(5655)

P1 = X(34312), P2 = X(20126) : reflections of X(476), X(5655) in X(2)

vertices of the Thomson triangle

P3 = X(34315) = {14,476} /\ {23,531} /\ {30,5463}

P4 = X(34316) = {13,476} /\ {23,530} /\ {30,5464}

Geometric properties :

K1138 is the third polar of X(2) in the bicircular quartic Q004. In other words, it is the locus of P whose polar line in Q004 passes through X(2).

K1138 is a central focal cubic whose center (and singular focus) is X(2). The inflexional tangent at X(2) passes through X(51).

The real asymptote is the Euler line.

See K065, another central focal cubic with center X(2).

K1138 is the Thomson isogonal transform of K912.

The Psi image of K1138 is also a central focal cubic with center X(2) passing through X(2), X(13), X(14), X(2782), X(5463), X(5464), X(9159), X(18332).