Cyrus the frog sits on a flat surface. He jumps, landing 2 feet away. He then chooses a direction at random and again jumps 2 feet. What is the probability that after the second jump Cyrus lands within 1 foot of his starting position?

**Answer Choices**

A. \dfrac{1}{6}

B. \dfrac{1}{5}

C. \dfrac{\sqrt{3}}{8}

D. \dfrac{\arctan \dfrac{1}{2}}{\pi}

E. \dfrac{2 \arcsin \dfrac{1}{4}}{\pi}