Given information:

The area of a circle decreases by 36%.

To find:

The percentage decrease in radius of the circle.

Solution:

Let the radius of the circle be 'r' and the area of the circle be 'A'.

The formula for the area of a circle is:

A = πr²

If the area of the circle decreases by 36%, then the new area of the circle will be:

New area = (100% - 36%) × Original area
New area = 64% × Original area

We know that the original area of the circle is A = πr². Substituting this in the above equation, we get:

New area = 64% × πr²

This gives us the new area of the circle. To find the new radius of the circle, we need to solve for 'r' in the above equation. We get:

New area = πr²
64% × πr² = πr²
0.64r² = r²
r² - 0.64r² = 0
0.36r² = 0
r = 0 (which is not possible) or r = √(0/0.36)
r = 0 or r = 0 (which is not possible)

We see that the above equation does not give us a valid solution for the new radius of the circle. This is because the area of the circle cannot decrease by 36% without changing the radius of the circle.

However, we can still find the percentage decrease in radius of the circle if we assume that the circumference of the circle remains constant. This is because the circumference of a circle is directly proportional to its radius. If the circumference remains constant, then the radius must decrease by the same percentage as the area.

The formula for the circumference of a circle is:

C = 2πr

If the circumference remains constant, then we have:

Original circumference = New circumference
2πr = 2πr'
r = r'

where r' is the new radius of the circle.

We know that the original area of the circle is A = πr². If the area of the circle decreases by 36%, then the new area of the circle will be:

New area = 64% × Original area
New area = 0.64πr²

We can solve for the new radius of the circle using the above equation. We get:

New area = πr'²
0.64πr² = πr'²
r'² = 0.64r²
r' = √(0.64) × r
r' = 0.8r

This means that the new radius of the circle is 80% of the original radius. Therefore, the percentage decrease in radius of the circle is:

Percentage decrease = (Original radius - New radius) / Original radius × 100%
Percentage decrease = (r - r') / r × 100%
Percentage decrease = (r - 0.8r) / r × 100%
Percentage decrease = 0.2 × 100%
Percentage decrease = 20%

Therefore, the percentage decrease in radius of the circle is 20%. Hence, option 'A' is the correct answer.