AMC 12 2003a Problem 16

A point P is chosen at random in the interior of equilateral triangle $ABC$. What is the probability that $\triangle ABP$ has a greater area than each of $\triangle ACP$ and $\triangle BCP$?

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