1.

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

Answer»

`9//16`
`3//4`
`1//2`
none of these

Solution :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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