There are no side lengths!

Geometry Level 3

Let \(ABC\) be a triangle with points \(P\) and \(Q\) respectively lying on line segments \(AB\) and \(BC\), such that \( \frac{AP}{PB} = 3 \) and \( \frac{BQ}{QC} = \frac{1}{2} \).

If lines \(AQ\) and \(CP\) intersect at \(R\), the ratio \( \frac{AR}{RQ} \) can be expressed as \( \frac{a}{b} \) where a and b are coprime integers. Find \( a + b \).


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