HMMT November 2009 F3

General 2
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Let $C$ be the circle of radius 12 centered at $(0,0)$ . What is the length of the shortest path in the plane between $(8 \sqrt{3}, 0)$ and $(0,12 \sqrt{2})$ that does not pass through the interior of $C$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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12+4 \sqrt{3}+\pi

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