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X(1), X(20), X(64), X(147), X(1297), X(1503), X(5000), X(5001), X(5018), X(7281)

Ia, Ib, Ic : vertices of the excentral triangle

cevian points of X(1503)

K270 is the isogonal circular pK with pivot X(1503), the infinite point of HK, with asymptote the parallel at X(1297) to HK, with singular focus X(112).

K270 belongs to the class CL035 of cubics. See also Table 6 and Table 55.