Question

The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumference of the circles.

Answer 1

Let the radii of the two circles be r₁ cm and r₂ cm.
Now,
Sum of the radii of the two circles = 7 cm

r1 + r2 = 7  ...............(i)

Difference of the circumferences of the two circles = 88 cm

⇒ 2πr₁ - 2πr₂ = 8

`=> 2pi("r"_1 - "r"_2) = 8`

`= ("r"_1 - "r"_2) = 8/(2pi)`

`=> "r"_1 - "r"_2 = (8)/(2xx22/7)`

`= "r"_1 - "r"_2 = (8xx7)/44`

`r_1 - r_2 = 56/44`

`r_1 - r_2 = 14/11``     .... (ii)

adding (i) and (ii), we get

`2"r"_1 = 91/11`

`"r"_1 = 91/22`

∴ Circumference of the first circle = 2πr1

`=2xx22/7xx91/22`

= 26 cm

Also,

`r_1 - r_2 =14/11`

`91/22-"r"^2 = 14/11` 

`91/22 - 14/11 = "r"_2`

`r_2 = 63/22`

∴ Circumference of the second circle = 2πr2

`= 2 xx 22/7xx63/22`

= 18 cm

Therefore, circumferences of the first and second circles are 18 cm and 26 cm, respectively.