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

Answer

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

### Step-by-Step Solution:

1. **Recall the formulas for Area and Circumference of a Circle:**
- The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
- The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]

2. **Set up the ratio of Area to Circumference:**
- We want to find the ratio \( \frac{A}{C} \):
\[ \frac{A}{C} = \frac{\pi r^2}{2 \pi r} \]

3. **Simplify the ratio:**
- We can cancel \( \pi \) from the numerator and the denominator:
\[ \frac{A}{C} = \frac{r^2}{2r} \]
- Next, we can simplify \( \frac{r^2}{2r} \) by canceling one \( r \):
\[ \frac{A}{C} = \frac{r}{2} \]

4. **Cross-multiply to find the relationship:**
- Rearranging the equation gives:
\[ 2A = Cr \]

5. **Conclusion:**
- The relationship between the area \( A \), circumference \( C \), and radius \( r \) of the circle is:
\[ 2A = Cr \]

### Final Answer:
The correct relationship is \( 2A = Cr \).