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X(1), X(3), X(4), X(376)

excenters

X2-OAP points, see Q003 and Table 53

K243 is the isogonal pK with pivot the reflection X(376) of G in O. Hence, it is a member of the Euler pencil of cubics. See Table 27.

K243 is the locus of point P such that the pedal triangle of P and the triangle of reflections of P in the vertices of ABC are perspective. See Table 6.