解:把△APC绕A逆时针旋转60°得到△AP"C",如图∴∠CAC"=∠PAP"=60°,AC=AC",AP=AP",PC=P"C,∴△APP"为等边三角形,∴PP"=AP,∵∠BAC=120°,∴∠BAC"=120°+60°=180°,即B,A,C"共线,∴BC"<BP+PP"+P"C,即AB+AC<AP+BP+CP.
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