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Question

Three circles of radii r1,r2 and r3 are drawn concentric to each other. The radii r1 and r2 are such that the area of the circle with radius r1 is equal to the area between the circles of radius r2 and r1. The area between the circles of radii r3 and r2 is equal to area between the circles of radii r2 and rr. What is the value of r1:r2:r3?
273194_3ffa1544571849a2a43e76b66650ecd0.png

A
1:2:3
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B
1:2:3
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C
1:2:3
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D
1:2:3
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Solution

The correct option is B 1:2:3
Given πr21=π(r22r12)
2r12=r22r12r22=12
r1r2=12r1:r2=1:2
andπ(r32r22)=π(r22r12)r32=2r22r12=2r22r222=3r222(2r12=r22)
r22r32=23r2r3=23r2:r3=2:3...(ii)
From (i) and (ii) r1:r2:r3=1:2:3

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