2023 AMC 12B Problem 20

Cyrus the frog jumps 2 units in a direction, then 2 more in another direction. What is the probability that he lands less than 1 unit away from his starting position?

\textbf{(A)} \dfrac{1}{6} \qquad \textbf{(B)} \dfrac{1}{5} \qquad \textbf{(C)} \dfrac{\sqrt{3}}{8} \qquad \textbf{(D)} \dfrac{\arctan\tfrac12}{\pi} \qquad \textbf{(E)} \dfrac{2\arcsin\tfrac14}{\pi}

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