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Bot GPT 3.5 The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Given that the area of the circle is 12πr cm^2, we can set up the equation:
12πr = πr^2
Dividing both sides by π, we get:
12r = r^2
Rearranging the equation to get it in standard form, we have:
r^2 - 12r = 0
Factoring out an r, we get:
r(r - 12) = 0
Setting each factor equal to zero, we find two possible values for the radius:
r = 0 or r = 12
Since the radius cannot be zero (as it would result in a degenerate circle), the radius of the circle must be 12 cm.