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X(1), X(4), X(222), X(223), X(269), X(347)

foci of the circum-conic (C) with center X(223), perspector X(57)

vertices of the intouch triangle

K713 is a circum-cubic that passes through the foci of the circum-conic (C) with center X(223), perspector X(57).

K713 meets :

• the line at infinity at the same points as pK(X6, X189),

• the circum-conic (C) at the same points as pK(X57, X77).

Remark : the pseudo-pole of K713 is the barycentric product of all these pairs of centers :

{X7, X221}, {X40, X269}, {X56, X347}, {X57, X223}, {X198, X279}, {X329, X1407}.