mikemcgarry
Attachment:
2-to-1 rectangle with circle.JPG
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) \(\frac{4-{\pi}}{4}\)
(B) \(\frac{4+{\pi}}{4}\)
(C) \(\frac{4+{\pi}}{8}\)
(D) \(\frac{8-{\pi}}{8}\)
(E) \(\frac{8+{\pi}}{8}\)
For a discussion of Geometric Probability, as well as a complete explanation of this particular question, see:
https://magoosh.com/gmat/2013/geometric- ... -the-gmat/Mike

Let the smaller side of square = 2x
Larger side will be = 4x
Radius of the circle will be = x
Area of the Square = 8\(x\)2
Area of the Circle = \(\pi\)\(x\)2
the probability that the point is inside the circle = Area of the Circle/ Area of the Square
= (\(\pi\)\(x\)2)/ (8\(x\)2)
= \(\pi\)/8
the probability that the point is
not inside the circle = 1 - the probability that the point is inside the circle
= 1- \(\pi\)/8
Answer D
Hope it helps