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Let ABCABCABC be a triangle with points PPP and QQQ respectively lying on line segments ABABAB and BCBCBC, such that APPB=3 \frac{AP}{PB} = 3 PBAP=3 and BQQC=12 \frac{BQ}{QC} = \frac{1}{2} QCBQ=21.
If lines AQAQAQ and CPCPCP intersect at RRR, the ratio ARRQ \frac{AR}{RQ} RQAR can be expressed as ab \frac{a}{b} ba where a and b are coprime integers. Find a+b a + b a+b.
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