Problem 91

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Problem 91: (2001 AMC 12, 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}$

Solution

Exercise 91: Solution

A point $P$ is selected at random from the interior of the pentagon with vertices $A=(0,2)$, $B=(5,0)$, $C=\left(2\pi+\frac54,0\right)$, $D=\left(2\pi+\frac54,4\right)$, and $E=(0,4)$. What is the probability that $\angle APB$ is obtuse?

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