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Question

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is

A
(2+3)r
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B
(2+3)3r
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C
(23)3r
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D
(23)r
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Solution

The correct option is A (2+3)3r
DEF is equilateral with side 2r,
if radius of circumcircle DEF is R1
Then area of DEF=34(2r)2
=3r2=2r.2r.2r4R1R1=2r3
Radius of the circle touching all the three given circles
=r+R1=r+2r3=(2+3)3r

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