Problem

Source: China Zongqing , 17 Aug 2014

Tags: inequalities proposed, inequalities



In the plane, Point $ O$ is the center of the equilateral triangle $ABC$ , Points $P,Q$ such that $\overrightarrow{OQ}=2\overrightarrow{PO}$. Prove that\[|PA|+|PB|+|PC|\le |QA|+|QB|+|QC|.\]