2025 AMC 8 Problem 12

The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?

\textbf{(A)} 3\pi \qquad \textbf{(B)} 4\pi \qquad \textbf{(C)} 5\pi \qquad \textbf{(D)} 6\pi \qquad \textbf{(E)} 8\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.