Parallelogram Problem

Geometry Level 5

ABCD ABCD is a parallelogram. Point PP on ABAB divides it in the ratio AP:PB=3:2 AP : PB = 3 : 2 , and point QQ on CDCD divides it in the ratio CQ:QD=7:3 CQ : QD = 7 : 3 . Let RR be the intersection of PQ PQ and ACAC. Then, AR:AC=a:b AR : AC = a : b , where aa and bb are positive coprime integers. What is a+ba + b ?

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