IMO 1988 LL FRA13

Let T be a triangle with inscribed circle C. A square with sides

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IMO 1988 LL FRA13

Origin: FRA

Problem

Let T be a triangle with inscribed circle C. A square with sides of length a is circumscribed about the same circle C. Show that the total length of the parts of the edges of the square interior to the triangle T is at least 2a.