Read the given information and statements carefully and decide which option is correct with respect to the statements.

If a circle has a radius (r), area (A) and circumference (C), then:

Statements:

1. A : $$\text{C}^2$$​ = 1 : 4π

2. A : C = r : 2

Correct option is D

Given :

We are provided with the following relationships related to a circle:

r = radius of the circle

A = area of the circle

C = circumference of the circle

Formula Used:

Area of a circle:

A = $$\pi r^2$$​

Circumference of a circle:

C = $$2\pi r$$

Solution:

Statement 1: $$\frac{A}{C^2} = \frac{1}{4\pi}$$​​

​$$\frac{A}{C^2} = \frac{\pi r^2}{(2\pi r)^2} = \frac{\pi r^2}{4\pi^2 r^2}$$​

​$$\frac{A}{C^2} = \frac{1}{4\pi}$$​

So, Statement 1 is correct.

Statement 2: $$\frac{A}{C} = \frac{r}{2}$$​​

​$$\frac{A}{C} = \frac{\pi r^2}{2\pi r} = \frac{r}{2}$$​

So, Statement 2 is also correct.

Both statements are correct.