2021 · Q62
Two circles touch externally. The sum of their areas is 41π square cm. If the distance between their centres is 9 cm, then what is difference between their diameters ?
Elementary MathematicsCircles
- A1 cm
- B1.5 cm
- C2 cm
- D4 cm
Explanation
Let the radii be r₁, r₂ with r₁ + r₂ = 9 and π(r₁² + r₂²) = 41π. Then (r₁+r₂)² = 81 = 41 + 2r₁r₂ gives r₁r₂ = 20, and (r₁−r₂)² = 41 − 40 = 1, so r₁ − r₂ = 1. The difference of diameters is 2(r₁ − r₂) = 2 cm, option (c).