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Question

Two circles of radii 'a' and 'b' touching each other externally, are inscribed in the area bounded by y=1x2 and the x-axis. If b=12, then a is equal to

A
14
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B
18
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C
12
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D
12
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Solution

The correct option is D 14

Given area x2+y2=1 and x-axis

i.e. upper semicircle

According to the diagram

B1D=B2D=1

C1D=1a,C2D=1b=12

A1C1=a,A2C2=b=12

C1A1D=C2A2D=90

By Pythagoras theorem

A1D=(C1D)2(A1C1)2

=(1a)2a2=12a

A2D=1414=0

C1=(A1D,a)=(12a,a)

C2=(A2D,b)=(0,12)

Since the circles touch each other

C1C2=r1+r2

C1C22=(a+12)2

(12a)+(a12)2=(a+12)2

12a=2a

a=14


881398_116897_ans_8b0feea7aca748bd979591e54efe7a23.png

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