Before jumping into the solution, I want to share the origins of the bizarre expression used frequently in the worlds of boxing and wrestling. In short, boxing rings were circular centuries ago. In 1838, the first square ring was introduced (thanks Wikipedia!). So, despite the fact that modern boxing rings are square, they are often referred to as square circles for historical reasons.
Now, what ratio of the identical areas of concentric square and circle shapes is shared? One straight forward method is shown below:
