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Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained inside both triangles XYZ and X'Y'Z'.  Find A/[XYZ].

 
 May 20, 2024

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