51

Part of 1986 IMO Longlists

Problems(1)

IMO Long List 1986 geometric inequality

Source:

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.

inequalitiesgeometryrectangletrigonometrycyclic quadrilateralgeometry proposed