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

Given Sum of the radius of the circles = 7 cm

the difference of their circumference = 8 cm

Let the radius one circle be ‘r_{1}’ cm and other be ‘r_{2}’ cm and circumference be ‘C_{1}’ and ‘C_{2}’ respectively.

Also, circumference of circle = 2πr

Where r = radius of the circle

C_{1} = 2πr_{1} and C_{2} = 2πr_{2}

r_{1} + r_{2} = 7 → eqn1

C_{1} – C_{2} = 8 → eqn2

(Note: Her it is considered that r_{1}>r_{2})

We can rewrite equation 2 as,

2πr_{1} – 2πr_{2} = 8

⇒ 2π(r_{1} – r_{2}) = 8

(taking 2π common from L.H.S)

Put the value of r_{1} from equation 3 in equation 1

(taking 11 as LCM on R.H.S)

Put value of r_{2} in equation 3

(from equation 3)

(taking 22 as LCM on R.H.S)

(by putting value of r_{1})

= 182/7

= 26 cm

(by putting value of r_{2})

= 126/7

= 18 cm

The circumference of circles are 26 cm and 18 cm.

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