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K529

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X(1), X(4), X(80), X(355), X(517), X(5903), X(14987)

S = X(14987), on the circumcircle and on the line X(100)-X(355), the tangential of X(355).

A', B', C' on the Fuhrmann circle and on the altitudes (see Honsberger's episodes p.52)

K529 is the locus of pivots of circular pKs whose orthic line passes through the incenter X(1). See CL035.

For example, with pivots X(1), X(80) we obtain K206, K058.

K529 is a circular focal cubic with focus X(80).

K529 is a member of the pencil of circular circum-cubics passing through X(1), X(4), X(80), X(517). This pencil is generated by K334 and the union of the line at infinity with the Feuerbach hyperbola. See also K681, K682, K683, K684, K685.