The area of a circle of radius r is πr^2. The perimieter of a circle of radius r is 2πr. Thus, if the area of a circle is equal to its perimeter, then we must have πr^2 = 2πr, where r is the radius.
Dividing both sides by π gives r^2 = 2r. Dividing both sides by r gives r = 2. So this circle must have a radius of 2.
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