2022 · Q88
Two circles touch externally. The sum of their areas is 89π square cm and the distance between their centres is 13 cm. What is the difference in their radii?
Elementary MathematicsCircles
- A2 cm
- B2.5 cm
- C3 cm
- D3.5 cm
Explanation
r₁+r₂ = 13 and r₁²+r₂² = 89 give (r₁−r₂)² = 89−(169−89) = 9, so the radii differ by 3 cm. The trap is to solve r₁+r₂ = 13 and r₁r₂ = 40 and then mis-subtract; squaring the difference directly is cleaner. The keyed option is C.