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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? [CBSE 2011]

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Solution

Let the diameter of the required circle be d.
Now, Area of circle = 2 ⨯ Circumference of the circle
πd22=22π×d2d22=2dd2=8dd2-8d=0dd-8=0d=8 cm d0
Hence, the diameter of the of the circle is 8 cm.

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