Question

Two circles touch each other externally. The sum of their areas is 490 π cm². Their centres are separated by 28 cm. The difference of their perimeters is ______.

Answer 1

Two circles touch each other externally. The sum of their areas is 490 π cm². Their centres are separated by 28 cm. The difference of their perimeters is 28π cm.

Explanation:

Let the radii be r₁, r₂.

Since the circles touch externally, r₁ + r₂ = 28.

Given π(r₁² + r₂²) = 490π, so r₁² + r₂² = 490. 

Then (r₁ + r₂)² = r₁² + r₂² + 2r₁r₂

⇒ 28² = 490 + 2r₁r₂

⇒ r₁r₂ = 147

Now (r₁ – r₂)² = r₁² + r₂² – 2r₁r₂

= 490 – 294

= 196 

⇒ r₁ – r₂ = 14

Difference of perimeters = 2π(r₁ – r₂) 

= 2π·14

= 28π cm