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10-1.Circle and System of Circles
normal
Two orthogonal circles are such that area of one is twice the area of other. If radius of smaller circle is $r$, then distance between their centers will be -
A
$\sqrt 3 r$
B
$2r$
C
$\sqrt 5 r$
D
$3r$
Solution
$\pi r_1^2 = 2\pi {r^2} \Rightarrow {r_1} = \sqrt 2 r$
$ \Rightarrow r_1^2 + {r^2} = {c_1}c_2^2$
$ \Rightarrow {c_1}{c_2} = \sqrt 3 r$
Standard 11
Mathematics
