If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius.

Explanation

To prove that the perimeter (circumference) of a circle varies inversely as the radius when the area increases at a uniform rate, we can follow these steps:

### Step 1: Understand the relationship between area and radius
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius.
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