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Inequality in a quadrilateral

Source: Baltic Way 2014, Problem 15

November 11, 2014
inequalitiestriangle inequalitygeometry proposedgeometry

Problem Statement

The sum of the angles AA and CC of a convex quadrilateral ABCDABCD is less than 180∘.180^{\circ} . Prove that AB⋅CD+AD⋅BC<AC(AB+AD).AB \cdot CD + AD \cdot BC < AC(AB + AD).
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