UPSC CDS 2 2022 Math Paper

Area of a circle =πx2
Where x= radius of the circleLet the radii of two circles be R and r
According to the question:
R+r=13‌cm‌‌⋯−(i)
Also, πR2+πr2=89π
⇒R2+r2=89
We know that
(R+r)2=R2+r2+2R
⇒169=89+2‌Rr
⇒Rr=40
From (i) and (ii), we get
⇒R(13−R)=40
⇒R2−13R+40=0
⇒(R−8)(R−5)=0
⇒R=8,5;r=5,8
Difference between their radii = 3 cm