2014 Cayley Problem 23

Three friends are in the park. Bob and Clarise are standing at the same spot and Abe is standing 10 m away. Bob chooses a random direction and walks in this direction until he is 10 m from Clarise. What is the probability that Bob is closer to Abe than Clarise is to Abe?

\textbf{(A)}\ \frac{1}{2}\quad \textbf{(B)}\ \frac{1}{3}\quad \textbf{(C)}\ \frac{1}{\pi}\quad \textbf{(D)}\ \frac{1}{4}\quad \textbf{(E)}\ \frac{1}{6}

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 Cayley contests here.