UPSC 2016 CDS II Math Paper

Remember:
If the two circles touch externally, then the distance between their centres is equal to the sum of their radii.
Let the radii of the given circles be x cm and (14 – x) cm.
∴πx2+π(14−x)2=130π
⇒x2+196+x2−28x=130
⇒2x2−28x+66=0
⇒x2−14x+33=0
⇒(x−11)(x−3)=0
⇒x=11,3
Thus, the difference in the radii ofthe circles is 8 cm