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Question

# A circle S of radius 'a' is the director circle of another circle S1. S1 is the director circle of circle S2 and so on. If the sum of the radii of all these circles is 2, then the value of a is

A
2+2
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B
22
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C
21/2
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D
2+1/2
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Solution

## The correct option is B 2−√2Director circle is the locus point of intersection of tangent If r is the radius of circle then √2r is the radius of the director circle Given radius of S=a Then radius of S1=a√2 S2=a√2√2 Sn=Sn−1√2 Sum = a+a√2+a2+a2√2…… Sum of infinite GP = a1–r=a1−12=2 2=√2a√2−1 a=2−√2

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