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2022 AMC 10A Problems/Problem 5

Revision as of 19:47, 11 November 2022 by Turtle09 (talk | contribs) (Created page with "==Problem 5== Square <math>ABCD</math> has side length <math>1</math>. Points <math>P</math>, <math>Q</math>, <math>R</math>, and <math>S</math> each lie on a side of <math>A...")
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Problem 5

Square $ABCD$ has side length $1$. Points $P$, $Q$, $R$, and $S$ each lie on a side of $ABCD$ such that $APQCRS$ is an equilateral convex hexagon with side length $s$. What is $s$?

$\textbf{(A) } \frac{\sqrt{2}}{3} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } 2 - \sqrt{2} \qquad \textbf{(D) } 1 - \frac{\sqrt{2}}{4} \qquad \textbf{(E) } \frac{2}{3}$

Solution

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