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Question
The side of a square is 10 cm. Find the area of the circumscribed circle. [π = 3.14]
Solution
If a circle is circumscribed in a square, then the diagonal of the square is equal to the diameter of the circle.
Diagonal of the square of the suquare `= sqrt(2)xx"Side of the square"`
`= sqrt (2)xx10`
`= 10sqrt(2) "cm" `
Diagonal = Diameter `= 10 sqrt(2) "cm"`
∴ `r = 5sqrt(2) "cm"`
Now,
Area of the circumscribed circle = πr2
`= 3.14 × (5sqrt(2)) `
= 3.14 × 50
= 157 cm2
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