Q. 73.5( 18 Votes )

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.

Answer :

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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