IMO Shortlist 2013 problem G3


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21. rujna 2014.
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In a triangle ABC, let D and E be the feet of the angle bisectors of angles A and B, respectively. A rhombus is inscribed into the quadrilateral AEDB (all vertices of the rhombus lie on different sides of AEDB). Let \phi be the non-obtuse angle of the rhombus. Prove that \phi \leq \operatorname{max}\{ \angle BAC, \angle ABC \}.
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