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

Options

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.

Answer

C

Explanation

`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))`