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...
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)