Problem

Source: ELMO 2014 Shortlist A1, by Ryan Alweiss

Tags: inequalities, trigonometry, calculus, topology, three variable inequality



In a non-obtuse triangle $ABC$, prove that \[ \frac{\sin A \sin B}{\sin C} + \frac{\sin B \sin C}{\sin A} + \frac{\sin C \sin A}{ \sin B} \ge \frac 52. \]Proposed by Ryan Alweiss