Question 19
A disk of radius $1$ rolls all the way around 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 $a+b+c?$