# A geometry problem by Áron Bán-Szabó

Geometry Level 3

Point $$P$$ and $$Q$$ are on the $$AC, BC$$ sides, respectively. $$PQ$$ is parallel to $$AB$$. If $$PM=3$$ and $$MQ=2$$, where $$M$$ is the intersection of $$PQ$$ and the $$BD$$ median, then how long is $$AB$$?

The figure is not drawn to scale

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