There are no side lengths!

Geometry Level 3

Let ABCABC be a triangle with points PP and QQ respectively lying on line segments ABAB and BCBC, such that APPB=3 \frac{AP}{PB} = 3 and BQQC=12 \frac{BQ}{QC} = \frac{1}{2} .

If lines AQAQ and CPCP intersect at RR, the ratio ARRQ \frac{AR}{RQ} can be expressed as ab \frac{a}{b} where a and b are coprime integers. Find a+b a + b .


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