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C(1):x^(2)+y^(2)=r^(2)and C(2):(x^(2))/(...

`C_(1):x^(2)+y^(2)=r^(2)and C_(2):(x^(2))/(16)+(y^(2))/(9)=1` interset at four distinct points A,B,C, and D. Their common tangents form a peaallelogram A'B'C'D'.
If A'B'C'D' is a square, then the ratio of the area of circle `C_(1)` to the area of circumcircle of `DeltaA'B'C'` is

A

`9//16`

B

`3//4`

C

`1//2`

D

none of these

Text Solution

Verified by Experts

If A'B'C'D' is a square, then tangents are
`y=+-x+-5`
for which diagonal length A'C' is 10.
Then the area of circumericle of `DeltaA'B'C' "is"25pi`
Also, the area of the circle `C_(1)` is `25//pi` . Hence the require ration is 1/2
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