2001 AMC 12 Problem 17

A point P is selected at random from the interior of the pentagon with vertices A = (0,2), B = (4,0), C = (2 \pi + 1, 0), D = (2 \pi + 1,4), and E=(0,4). What is the probability that \angle APB is obtuse?

\text{(A) }\frac {1}{5} \qquad \text{(B) }\frac {1}{4} \qquad \text{(C) }\frac {5}{16} \qquad \text{(D) }\frac {3}{8} \qquad \text{(E) }\frac {1}{2}

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