Question 37051
A circle with radius of square root of 2 units is circumscribed about a square with side length 2 units. Find the probability that a randomly chosen point will be inside the circle but outside the square

Draw the picture of the square inside the circle.
Area of the circle is (pi)(sqrt2)^2=2pi
Area of square is 2^2=4
Area in the circle but not in the square = 2pi-4

Probability of a point being in the circle but not
in the square = (2pi-4)/2pi = (pi - 2)/pi = 1-2/pi
Cheers,
Stan H.