# 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 ‘r1’ cm and other be ‘r2’ cm and circumference be ‘C1’ and ‘C2’ respectively.

Also, circumference of circle = 2πr

Where r = radius of the circle

C1 = 2πr1 and C2 = 2πr2

r1 + r2 = 7 eqn1

C1 – C2 = 8 eqn2

(Note: Her it is considered that r1>r2)

We can rewrite equation 2 as,

2πr1 – 2πr2 = 8

2π(r1 – r2) = 8

(taking 2π common from L.H.S)      Put the value of r1 from equation 3 in equation 1    (taking 11 as LCM on R.H.S)   Put value of r2 in equation 3 (from equation 3) (taking 22 as LCM on R.H.S)  (by putting value of r1)   = 182/7

= 26 cm (by putting value of r2)   = 126/7

= 18 cm

The circumference of circles are 26 cm and 18 cm.

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