Australian AMC 2017 - Senior Question 24

Question 24

A circle touches one side of a square and passes through the end vertices of the opposite side. The circle has circumference $c$ and the square has perimeter $s$. Which of the following is true to the nearest one percent?

Question illustration

$c$ is approximately 5% larger than $s$.
$c$ is approximately 2% larger than $s$.
$c$ and $s$ are equal.
$c$ is approximately 2% smaller than $s$.
$c$ is approximately 5% smaller than $s$.