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X(2), X(253), X(3146), X(14572)

foci of the Steiner circum-ellipse

K347 is another pK passing through the foci of the Steiner circum-ellipse. See K007, the Lucas cubic.

Its pole is X(14572), the barycentric product of X(253) and X(3146). Note that this pole lies on the curve.

K347 is the locus of contacts of tangents drawn through X(3146) to the circum-conics passing through X(253) i.e. the isotomic transforms of the lines passing through X(20).