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3 circles of radii a,b,c (a<b<c) touch e...

3 circles of radii `a,b,c (a

A

`1/(sqrt(b))=1/(sqrt(a))+1/(sqrt(c))`

B

`a,b,c` are in A.P

C

`1/(sqrt(a))=1/(sqrt(b))+1/(sqrt(c))`

D

`sqrt(a),sqrt(b),sqrt(c)` are in A.P.

Text Solution

Verified by Experts

The correct Answer is:
C

`DeltaAMP: sqrt((a+b)^(2)-(b-a)^(2))=MP`………i
`DeltaCPN:sqrt((c+a)^(2)-(c-a)^(2))=PN`……….ii
`DeltACR:sqrt((c+b)^(2)-(c-b)^(2))=AR`…..ii
From i,ii and ii
`MP+PN=ARimplies2sqrt(aB)+2sqrt(ac)=2sqrt(bc)implies1/(sqrt(c))+1/(sqrt(b))=1/(sqrt(a))`
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