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Question

As shown in figure, three circles which have the same radius r, have centres at (0,0),(1,1) and (2,1). If they have a common tangent line, as shown, then the value of radius is


A
125 units
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B
15 units
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C
5 units
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D
5 units
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Solution

The correct option is A 125 units

Given centres are (0,0),(1,1) and (2,1)
The tangent is parallel to the line joining (0,0) and (2,1)
m=1020=12
Assuming the tangent line as
x2y+c=0(1)
Internal point of simlitude lies on transverse common tangents
Hence it will pass through mid point (1,1) and (2,1) i.e., (3/2,1) ( circles have equal radius)
putting the value in (1) we get
c=1/2
Now using tangency condition
r=1/21+4=125 units

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