HMMT 2010 F9

General 2
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You are standing in an infinitely long hallway with sides given by the lines $x=0$ and $x=6$ . You start at $(3,0)$ and want to get to $(3,6)$ . Furthermore, at each instant you want your distance to $(3,6)$ to either decrease or stay the same. What is the area of the set of points that you could pass through on your journey from $(3,0)$ to $(3,6)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

Also HMMT 2010 G7.

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9 \sqrt{3}+\frac{21 \pi}{2}

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