For the three circles with centers A, B and C and radii 5 cm, 2 cm and 6 cm respectively.

Assertion (A) : To find the perimeter of the triangle ABC, add the radii of given three circles.

Reason (R) : The required perimeter is the product of sum of radii by 2.

1. A is true, R is true

2. A is true, R is false

3. A is false, R is true

4. A is false, R is false

Let the circles intersect at points D, E and F.

From figure,

Perimeter of triangle ABC = AB + BC + CA

= (AD + BD) + (BE + CE) + (CF + FA)

= 5 + 2 + 2 + 6 + 6 + 5

= 26 cm.

On adding radii of three circles, we get :

5 + 2 + 6 = 13 cm, which is not equal to perimeter.

Sum of radii × 2 = 13 × 2 = 26 cm, which is equal to perimeter.

∴ A is false, R is true

Hence, Option 3 is correct option.