2021 Fall AMC 10A Problems/Problem 19

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$19$. A disk of radius $1$ rolls all the way around in the inside of a square of side length $s>4$ and sweeps out a region of area $A$. A second disk of radius $1$ rolls all the way around the outside of the same square and sweeps out a region of area $2A$. The value of $s$ can be written as $a + \dfrac{b\pi}{c}$, where $a,b,$ and $c$ are positive integers and $b$ and $c$ are relatively prime. What is $a+b+c?$

$\textbf{(A) }10\qquad\textbf{(B) }11\qquad\textbf{(C) }12\qquad\textbf{(D) }13\qquad\textbf{(E) }14$

See Also

2021 Fall AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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All AMC 10 Problems and Solutions

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