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Products of sides and diagonals in a quadrilateral

Source: South African MO 2008 Q2

May 27, 2012
geometry unsolvedgeometry

Problem Statement

Let ABCDABCD be a convex quadrilateral with the property that ABAB extended and CDCD extended intersect at a right angle. Prove that AC⋅BD>AD⋅BCAC\cdot BD>AD\cdot BC.
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