Question

Three circles with centres A, B and C and radii 5 cm, 2 cm and 6 cm respectively and touch each other externally.

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 the sum of the radii and 2.

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

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