If the area of a circle is A, radius of the circle is r and circumference of it is C, then

Options

A. `(A)/(r )=C`
B. `r C = rA`
C. `(C)/(A) = (r )/(2)`
D. `AC = (r^(2))/(4)`

Answer

To solve the problem, we need to establish the relationships between the area (A), radius (r), and circumference (C) of a circle.

### Step-by-Step Solution:

1. **Understand the formulas:**
- The area of a circle is given by the formula:
\[ A = \pi r^2 \]
- The circumference of a circle is given by the formula:
\[ C = 2\pi r \]

2. **Set up the relationship between C and A:**
- We want to find the relationship between the circumference (C) and the area (A). To do this, we can divide the circumference by the area:
\[ \frac{C}{A} = \frac{2\pi r}{\pi r^2} \]

3. **Simplify the expression:**
- In the expression \(\frac{C}{A}\), we can simplify it by canceling out \(\pi\) from the numerator and denominator:
\[ \frac{C}{A} = \frac{2r}{r^2} \]
- Now, we can simplify further by canceling \(r\) from the numerator and denominator:
\[ \frac{C}{A} = \frac{2}{r} \]

4. **Conclusion:**
- From the above simplification, we find that:
\[ C = \frac{2A}{r} \]
- Thus, the relationship we derived is:
\[ \frac{C}{A} = \frac{2}{r} \]

### Final Answer:
The correct relationship is:
\[ \frac{C}{A} = \frac{2}{r} \]