IMO 1985 LL BRA7

A convex quadrilateral is inscribed in a circle of radius 1. Prove

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IMO 1985 LL BRA7

Origin: BRA

Problem

A convex quadrilateral is inscribed in a circle of radius 1. Prove that the difference between its perimeter and the sum of the lengths of its diagonals is greater than zero and less than 2.