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Question

(a)The sum of two radii of two circles is 140cm and the difference of their circumference is 88cm.Find the diameter of the circle.

(b)the sum of the two radii of two circles is 70cm and the difference of their curcumferences is 8 cm.Find the circumference.

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Solution

a) let radii of two circle be r1 and r2

r1 + r2 = 140 ………………(1)

circumfrence1 – circumference2 = 88

2r1 - 2r2 = 88

2( r1 – r2 ) = 88

r1 – r2 =

r1 – r2 =

r1 – r2 = 14 …………………(2)

adding eqn (1) and (2)

2 r1 = 154

r1 = 154/2 = 77 cm

put this value in eqn (1)

we get, 77 + r2 = 140

r2 = 140 – 77

r2 = 63 cm

b) let radii of two circle be r1 and r2

r1 + r2 = 70 ………………(1)

circumfrence1 – circumference2 = 88

2r1 - 2r2 = 88

2( r1 – r2 ) = 88

r1 – r2 =

r1 – r2 =

r1 – r2 = 14 …………………(2)

adding eqn (1) and (2)

2 r1 = 84

r1 = 84/2 = 42cm

put this value in eqn (1)

we get, 42 + r2 = 70

r2 = 70 – 42

r2 = 28 cm


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