2021 Pascal Problem 14

Nate has a grid made of shaded and unshaded 2 cm by 2 cm squares, as shown. He randomly places a circle with a diameter of 3 cm on the board so that the centre of the circle is at the meeting point of four squares. What is the probability that he places the disk so that it is touching an equal number of shaded and unshaded squares?

\textbf{(A)}\ \frac{13}{25}\quad \textbf{(B)}\ \frac{17}{25}\quad \textbf{(C)}\ \frac{11}{25}\quad \textbf{(D)}\ \frac{21}{25}\quad \textbf{(E)}\ \frac{3}{5}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.