In the diagram above, the sides of rectangle \(ABCD\) have a ratio \(AB:BC = 1:2,\) and the circle is tangent to three

[Gmat_mission]

In the diagram above, the sides of rectangle \(ABCD\) have a ratio \(AB:BC = 1:2,\) and the circle is tangent to three sides of the rectangle. If a point is chosen at random inside the rectangle, what is the probability that it is not inside the circle?

(A) \(\dfrac{4-\pi}4\)
(B) \(\dfrac{4+\pi}4\)
(C) \(\dfrac{4+\pi}8\)
(D) \(\dfrac{8-\pi}8\)
(E) \(\dfrac{8+\pi}8\)

Answer: D

Source: Magoosh