HMMT November 2016 T1

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Two circles centered at $O_{1}$ and $O_{2}$ have radii 2 and 3 and are externally tangent at $P$ . The common external tangent of the two circles intersects the line $O_{1} O_{2}$ at $Q$ . What is the length of $P Q$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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