Two circles touch internally. The sum of their areas is 116$\pi$ cm² and the distance between their centres is 6 cm. The radii of the circles are respectively–

Explanation

According to the question- (r₁ – r₂) = 6 cm ...... (i) $\pi r_1^2 + \pi r_2^2 = 116\pi$ $r_1^2 + r_2^2 = 116$ ...... (ii) from equation (i)– (r₁ – r₂)² = 6² $r_1^2 + r_2^2 - 2r_1r_2 = 36$ 116 – 2r₁r₂ = 36 2r₁r₂ = 80 Now (r₁ + r₂)² = r₁² + r₂² + 2r₁r₂ (r₁ + r₂)² = 116 + 80 (r₁ + r₂)² = 196 r₁ + r₂ = 14 .......... (iii) from (i) and (iii) – 2r₁ = 20 cm r₁ = 10 cm again 2r₂ = 8 cm r₂ = 4 cm Hence, option (b) is the right answer.