If the area of a circle is numerically equal to twice its circumference, then what is the diameter of the circle?

Given:

Area of circle = 2 × Circumference of circle …… (i)

Let the radius of the circle be ‘r’.

Then, the area of the circle = πr^{2}

and the circumference of the circle = 2πr

Using (i), we have

πr^{2} = 2 × 2πr

πr^{2} = 4πr

r = 4 cm

∵ Diameter = 2 × radius

∴ Diameter = 2 × 4

= 8 cm

__Hence, the diameter of the circle is 8 cm.__

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