Question 17A 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? $\dfrac{1}{5}$$\dfrac{1}{4}$$\dfrac{5}{16}$$\dfrac{3}{8}$$\dfrac{1}{2}$
