Question

Two circles touch each other externally. The sum of their areas is `490pi cm^2`. Their centres are separated by `28 cm`. Find the difference of their radii (in cm)
A. 14
B. 7
C. 10.5
D. 3.5

Answer 1

Correct Answer - A
Let the radii of the circles be denoted by `r_(1)` cm and `r_(2)` cm where `r_(1) ge r_(2)`. As the circles touch each other externally, distance between their centres = Sum of their radii.
` :. R_(1)+r_(2)=28 " (1)" `
Also `pi(r_(1))^(2)+pi(r_(2))^(2)=490 pi`
` :. (r_(1))^(2)+(r_(2))^(2)=490 " (2)" `
Squaring both sides of Eq. (1), we get
`(r_(1))^(2)+(r_(2))^(2) + 2(r_(1))(r_(2))=784`
`r_(1)*r_(2)=147 " (3)" `
Solving Eqs. (1) and (3), we get
`r_(1)=21 and r_(2) =7. ( :. r_(1) ge r_(2))`
` :. ` Required difference = 14 cm.