Question

The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13.2 cm. Find the radii of the two circles.

Answer 1

Let r₁ and r₂ be the radii of two circles.
⇒ r₁ + r₂ = 10.5     ....(i)
And,
`2π"r"_(6.3-4.21) - 2π"r"_2` = 13.2

⇒ `2 xx (22)/(7) xx ("r"_1 - "r"_2)` = 13.2

⇒ r₁ - r₂ = `(13.2 xx 7)/(2 xx 22)`
⇒ r₁ - r₂ = 2.1    ....(ii)
Adding (i) and (ii), we get
2r₁ = 12.6
⇒ r₁ = 6.3cm
Now,
r₁ - r₂ = 2.1
⇒ 6.3 - r₂ = 2.1
⇒ r₂ = 4.2cm.