IMO 1986 LL MON51

Let a, b, c, d be the lengths of the sides of a quadrilateral

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IMO 1986 LL MON51

Origin: MON

Problem

Let a, b, c, d be the lengths of the sides of a quadrilateral circumscribed about a circle and let S be its area. Prove that S \leq \sqrt abcd and find conditions for equality.