AoPS Wiki:Problem of the Day/August 9, 2011

Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?

$\textbf{(A)}$ $\frac{1}{36}$ $\textbf{(B)}$ $\frac{1}{24}$ $\textbf{(C)}$ $\frac{1}{18}$ $\textbf{(D)}$ $\frac{1}{12}$ $\textbf{(E)}$ $\frac{1}{9}$