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CWMO 2014 Problem 7

    In the plane, Point OO is the center of the equilateral triangle ABCABC , Points P,QP,Q such that OQ→=2PO→\overrightarrow{OQ}=2\overrightarrow{PO} . Prove that∣PA∣+∣PB∣+∣PC∣≤∣QA∣+∣QB∣+∣QC∣.|PA|+|PB|+|PC|\le |QA|+|QB|+|QC|.

    Dataset text AI-MO AoPS. Quoted with source.

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