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Question
If the area of the circle is numerically equal to twice its circumference then what is the diameter of the circle?
Solution
Let the diameter of the required circle be d.
Now, Area of circle = 2 ⨯ Circumference of the circle
`=> pi("d"/2)^2 =2(2pixxd/2)`
`=>(d/2)^2 =2"d"`
⇒ d2 = 8d
⇒ d2 - 8d = 0
⇒ d (d - 8) = 0
⇒ d = 8 cm [∴ d ≠ 0 ]
Hence, the diameter of the of the circle is 8 cm.
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