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Question

A circle with area A1 is contained in the interior of a larger circle with area A1+A2. If the radius of the larger circle is 3 and A1,A2,A1+A2 are in A.P., what is the radius of the smaller circle?

A
32
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B
23
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C
3
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D
32
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Solution

The correct option is B 3

Area of small circle =A1
Area of larger circle =A1+A2
Given that
(A1,A2,A1+A2) form an AP
Common difference
d=A2A1=A2+A1A2A2A1=A1A2=2A1(1)

Radius of larger circle =3 units
Area of larger circle =π(3)2=9π
A1+A2=9π
From (1)
2A1+A1=9π3A1=9πA1=3ππr2=3π
r=3 units

867730_507386_ans_2258bf2ff868488786a5b2a22816e804.png

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