If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Let `a` be the side of the square. By using the Pythagoras theorem, AB 2 \+ BC 2 = AC 2 ⇒ a 2 \+ a 2 = AC 2 ⇒ AC 2 = 2a 2 ⇒ AC = a Diagonal of the square = Diameter of the circle d = a Radius, r = = Now, the ratio of the area of the circle to the area of the square is: Hence, the ratio of the area of the circle to the area of the square is 11 : 7.