1st Balkan Mathematical Olympiad Problems 1984

1st Balkan Mathematical Olympiad Problems 1984A1.  Let x1, x2, ... , xn be positive reals with sum 1. Prove that x1/(2 - x1) + x2/(2 - x2) + ... + xn/(2 - xn) ≥ n/(2n - 1). A2.  ABCD is a cyclic quadrilateral.

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