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Question

Two circles touch each other externally. The sum of their areas is (106π)cm2 and the distance between their centers is 14 cm. Find the sum diameters of the circles.


A

14 cm

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B

15 cm

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C

28 cm

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D

30 cm

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Solution

The correct option is C

28 cm


Let the radius of bigger and smaller circle be 'R' and 'r' respectively.

Sum of areas =πR2+πr2=π(R2+r2)

According to question, π(R2+r2)=106π

R2+r2=106(I)

Also, R+r=14

R=14r(II)

Putting (II) in (I)

(14r)2+r2=106

196+r228r+r2=106

2r228r+90=0

r214r+45=0

r29r5r+45=0

r(r9)5(r9)=0

(r5)(r9)=0

r=9 or r=5

r=9 cm can't be possible because that means R=5 cm which can't be true for our assumption. So, r=5 cm and R=9 cm. Sum of diameters =(10+18) cm=28 cm


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