IMO 2013 Shortlist G3

In a triangle ABC, let D and E be the feet of the angle bisectors of angles A and B, respectively. A rhombus is inscribe...

IMO 2013 Shortlist G3

Category: Geometry

Problem

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 ϕ be the non-obtuse angle of the rhombus. Prove that ϕ ď maxt=BAC,=ABCu. (Serbia)