A square circumscribes a circle and another square is inscribed in the circle such that one vertex is at the point of contact. The ratio of the areas of the circumscribed and the inscribed squares is:

Correct option is A

Radius of the circle = R
Diameter of the circle, D = 2R

Formula used:
Area of square = (side)²

Solution:

For the circumscribed square (Ac):
Side of square, sc = D = 2R
=> Ac = (2R)² = 4R²

For the inscribed square (Ai):
Diagonal of square, di = D = 2R
Side of square = di / √2 = 2R / √2 = √2 R
=> Ai = (√2 R)² = 2R²

Ratio of areas:
Ac : Ai = 4R² : 2R² = 2 : 1

Correct answer is (a) 2 : 1