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Quad ineq

Source: Indian RMO 1997 Problem 4

October 26, 2005
geometryindiaRMOinequalities

Problem Statement

In a quadrilateral ABCDABCD, it is given that ABAB is parallel to CDCD and the diagonals ACAC and BDBD are perpendicular to each other. Show that (a) AD⋅BC≥AB⋅CDAD \cdot BC \geq AB \cdot CD (b) AD+BC≥AB+CD.AD + BC \geq AB + CD.
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