# 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 $$a + b$$.

Inspiration

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