The circle touch each other internally. The sum of their area is 116 pie cm² and the distance between their centres is 6 cm. Find the radii of the circles.

The correct answer is: 10 cm

It is given that the distance between their centres is 6 cm
 r₂ - r₁ = 6  r₂ = 6 + r₁
The sum of their area of two circles =  116  cm²
 (r₁)² +  (r₂)² = 116 
 [ (r₁)² + (6 + r₁)² ] = 116 
  (r₁)² + 36 +  (r₁)² + 12 r = 116
 2 (r₁)² + 12 r + 36 – 116 = 0
 2 (r₁)² + 12 r – 80 = 0  (r₁)² + 6 r – 40 = 0
Using splitting the middle term,
We get, (r₁)² + 10 r – 4r – 40 = 0
(r₁ + 10 )( r₁ – 4) = 0  r₁ = 4 , - 10
Since radius is always positive,  r₁ = 4 cm
r₂ = 4 + 6 = 10 cm