In reference to a circle the value of `pi` is equal to

Options

A. `("area")/("circumference")`
B. `("area")/("diameter")`
C. `("circumference")/("diameter")`
D. `("circumference")/("radius")`

Answer

To find the value of π (pi) in reference to a circle, we will evaluate the options given and determine which one correctly represents π.

### Step-by-Step Solution:

1. **Evaluate Option A: Area by Circumference**
- The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
- The circumference of a circle is given by the formula:
\[ \text{Circumference} = 2\pi r \]
- Now, if we take the ratio of the area to the circumference:
\[ \frac{\text{Area}}{\text{Circumference}} = \frac{\pi r^2}{2\pi r} \]
- Simplifying this:
\[ = \frac{r}{2} \]
- Since \(\frac{r}{2}\) is not equal to π, Option A is incorrect.

2. **Evaluate Option B: Area by Diameter**
- The diameter \(D\) of a circle is given by:
\[ D = 2r \]
- Taking the ratio of the area to the diameter:
\[ \frac{\text{Area}}{\text{Diameter}} = \frac{\pi r^2}{2r} \]
- Simplifying this:
\[ = \frac{\pi r}{2} \]
- Since \(\frac{\pi r}{2}\) is not equal to π, Option B is also incorrect.

3. **Evaluate Option C: Circumference by Diameter**
- Using the circumference and diameter:
\[ \frac{\text{Circumference}}{\text{Diameter}} = \frac{2\pi r}{2r} \]
- Simplifying this:
\[ = \pi \]
- Since this is equal to π, Option C is correct.

4. **Evaluate Option D: Circumference by Radius**
- Taking the ratio of circumference to radius:
\[ \frac{\text{Circumference}}{\text{Radius}} = \frac{2\pi r}{r} \]
- Simplifying this:
\[ = 2\pi \]
- Since \(2\pi\) is not equal to π, Option D is incorrect.

### Conclusion:
The correct answer is **Option C: Circumference by Diameter**, which equals π.