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IMO Shortlist 2013, Geometry #3

Source: IMO Shortlist 2013, Geometry #3

July 10, 2014
geometryrhombustrigonometryIMO Shortlist

Problem Statement

In a triangle ABCABC, let DD and EE be the feet of the angle bisectors of angles AA and BB, respectively. A rhombus is inscribed into the quadrilateral AEDBAEDB (all vertices of the rhombus lie on different sides of AEDBAEDB). Let φ\varphi be the non-obtuse angle of the rhombus. Prove that φ≤max⁡{∠BAC,∠ABC}\varphi \le \max \{ \angle BAC, \angle ABC \}.
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