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Question

A circle C1 of radius 2 touches both x-axis and y-axis. Another circle C2 whose radius is greater than 2 touches circle C1 and both the axes. Then the radius of circle C2 is

A
642
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B
6+42
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C
643
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D
6+43
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Solution

The correct option is B 6+42
The first circle touches both axes and radius is 2 units.

Hence center of the circle is (2,2)

Let the radius of other circle be a and this circle also touches both the axes.
Hence center of circle is (a,a)

This circle touches the first circle

Hence (a2)2+(a2)2=a+2

On squaring both the sides, we get

a212a+4=0a=12±(12)24×4×12

=12±1282=6±42

But a>2, therefore a=642 is neglected,

Hence, a=6+42.

387188_153024_ans.png

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