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What is the minimum possible value of AB/CD?

Source: Tuymaada 2009, Senior League, First Day, Problem 3

July 19, 2009
inequalitiesgeometrycyclic quadrilateralgeometry unsolved

Problem Statement

On the side AB AB of a cyclic quadrilateral ABCD ABCD there is a point X X such that diagonal BD BD bisects CX CX and diagonal AC AC bisects DX DX. What is the minimum possible value of ABCD AB\over CD? Proposed by S. Berlov
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