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Tapasranjan Das Grade: 12
```        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.P
2.G.P
3.H.P
4.A.G.P
5.None of these```
7 years ago

## Answers : (1)

147 Points
```										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 ,λ2 ,λ3  are 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 - 2λr acos θ -a2]1/2
=[ - 2λr acos θ ]1/2
so given λ1 ,λ2 ,λ3  are in GP
so   -2λ1 acos θ,-2λ2 acos θ,-2λ3 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
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

```
7 years ago
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