HMMT 2019 G3

Geometry
Answer

Let $A B$ be a line segment with length 2 , and $S$ be the set of points $P$ on the plane such that there exists point $X$ on segment $A B$ with $A X=2 P X$ . Find the area of $S$ .

Dataset text NuminaMath olympiads. Quoted with source.

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

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