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Longest line contained in the region

Source: ISI Entrance 2014, P6

May 11, 2014
rotationtrigonometryreal analysisreal analysis unsolved

Problem Statement

Define A={(x,y)∣x=u+v,y=v,u2+v2≤1}\mathcal{A}=\{(x,y)|x=u+v,y=v, u^2+v^2\le 1\}. Find the length of the longest segment that is contained in A\mathcal{A}.
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