In triangle \( ABC \), the point \( P \) divides \( BC \) internally in the ratio \( 3 : 4 \) and \( Q \) divides \( CA \) internally in the ratio \( 5 : 3 \). If \( AP \) and \( BQ \) intersect in a point \( G \), then \( G \) divides \( AP \) internally in the ratio
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Van Schooten's or Mass Point Geometry can solve these ratio problems very quickly.