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Q.

The circles of radii 4 and 9 touch externally, AB is a common tangent. The radius of the circle which touches the line AB and the two circles externally is

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a

2536

b

625

c

1297

d

3625

answer is D.

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Detailed Solution

AP+PB=AB           2r1r+2r2r=2r1r2   ( AB  = length of direct common tangent =r1+r22-r1-r22=2r1r2)r=r1r2r1+r2⇒r=r1r2(r1+r2)2=4×9(2+3)2=3625
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