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    Question

    A square is inscribed in a circle, and another square is

    circumscribed around the same circle. If the side of the inscribed square is 12 cm, find the difference between the areas of the two squares.
    A 72 cm² Correct Answer Incorrect Answer
    B 96 cm² Correct Answer Incorrect Answer
    C 108 cm² Correct Answer Incorrect Answer
    D 144 cm² Correct Answer Incorrect Answer

    Solution

    Let the side of the inscribed square be 12 cm. The diagonal of the square will be equal to the diameter of the circle. Diagonal of the inscribed square = √2 × side = √2 × 12 = 12√2 cm. The radius of the circle = (12√2) / 2 = 6√2 cm. For the circumscribed square, the side of the square is equal to the diameter of the circle, which  is 12√2 cm. Area of the inscribed square = (12)² = 144 cm². Area of the circumscribed square = (12√2)² = 288 cm². Difference in areas = 288 - 144 = 144 cm². Correct Option: c

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