# Q:-If the distances between the origin and centers of the three circles x2+y2 - 2λr x -a2=0 ; r=1,2,3 are in G.P then the lengths of tangents to the circles from any point on the circle x2+y2=a2 are in__________1.A.P2.G.P3.H.P4.A.G.P5.None of these

148 Points
14 years ago

Dear Tapasranjan

x2+y2 - 2λr x -a2=0

(x-λr)2 +y2 =a2 + λr2

center of circle( λr,0)

so distance of center from the origin. = λr

so λ1 2 ,λare in GP

now let a general point (acos θ ,asinθ) on circle x2+y2=a2

so length of tangent from this point to the given circle

= [(acos θ)2+(asinθ)2 - 2λacos θ -a2]1/2

=[ - 2λacos θ ]1/2

so given λ1 2 ,λare in GP

so   -1 acos θ,-2λ2 acos θ,-3 acos θ  will also be in GP

[ - 2λ1 acos θ ]1/2 , [ - 2λ2 acos θ ]1/2  , [ - 2λ3 acos θ ]1/2  will also be in GP

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