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

The figure is not drawn to scale

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