Question

If a circle is inscribed in a square, then

A
Area of the circleArea of the square=π2
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B
Area of the circleArea of the square=π4
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C
Circumference of the circlePerimeter of the square=π4
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D
Circumference of the circlePerimeter of the square=π2
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Solution

The correct option is C Circumference of the circlePerimeter of the square=π4 Let the radius of the circle and the side length of the square be r and s respectively. Step 1: Area of the circle =πr2 Circumference of the circle =2πr Step 2: Diameter of the circle =2×r Step 3: When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the side length of the square(s) is 2r. Step 4: Area of the square=s2=(2r)2=22×r2=4r2 Perimeter of the square=4×s=4×2r=8r Step 5: Area of the circle : Area of the square=πr2:4r2 Divide both sides by r2 =πr2r2:4r2r2 =π:4 Circumference of the circle : Perimeter of the square =2πr:8r Divide both sides by 2r =2πr2r:8r2r=π:4 Hence, options (b) and (c) are correct choices.

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