Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles is 24/7cm2. Find the radius of each circle.
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From the way the circles are drawn, each side a of the square is equal to twice the radius R of the circles.
So a = 2 R.
There is a quadrant of each circle inside the square. Hence area covered by 4 quadrants of circle = 4 * (22/7 * R²)/4 = 22/7 * R²
Area of square = a² = 4 R²
Shaded area between the circles = (4 - 22/7) R² = 24/7 cm² GIVEN
Hence, R = 2 cm
So a = 2 R.
There is a quadrant of each circle inside the square. Hence area covered by 4 quadrants of circle = 4 * (22/7 * R²)/4 = 22/7 * R²
Area of square = a² = 4 R²
Shaded area between the circles = (4 - 22/7) R² = 24/7 cm² GIVEN
Hence, R = 2 cm
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