Let the centre of the two circles be c1 and c2, then c1c2=9cm (given)
If r1 and r2 denotes the radii. Then, πr12+πr22=41π ⇒r12+r22=41 Also r1+r2=9 Put r2=9−r1 into Eq (i), we get ⇒ (ii) ⇒r12+(9−r1)2=41 ⇒r12+81+r12−18r1=41 ⇒2r12−18r1+40=0 ⇒r12−9r1+20=0 ⇒r12−4r1−5r1+20=0 ⇒r1(r1−4)−5(r1−4)=0 ⇒(r1−4)(r1−5)=0 ∴r1=4 or 5 When r1=4 ⇒r2=9−r1=9−4=5cm When r1=5 ⇒r2=9−r1=9−5=4cm For, r1=4cm and r2=5cm ⇒d1=2×4=8cm and d2=2×5=10cm ∴d2−d1=10−8=2cm Similarly, for r1=5cm and r2=4cm, the difference between the diameters is 2cm.