Question 22
A disk of radius $1$ rolls all the way around the inside of a square of side length $s \gt 4$ 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 $a + \frac{b\pi}{c}$, where $a$, $b$, and $c$ are positive integers and $b$ and $c$ are relatively prime. What is $a + b + c$?