# Parallelogram Problem

Geometry Level 5

$$ABCD$$ is a parallelogram. Point $$P$$ on $$AB$$ divides it in the ratio $$AP : PB = 3 : 2$$, and point $$Q$$ on $$CD$$ divides it in the ratio $$CQ : QD = 7 : 3$$. Let $$R$$ be the intersection of $$PQ$$ and $$AC$$. Then, $$AR : AC = a : b$$, where $$a$$ and $$b$$ are positive coprime integers. What is $$a + b$$?

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