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

Explanation

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

### Step-by-Step Solution:

1. **Define the Area of the Circle**:
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
...