Question

Circle I passes through the centre of, and is tangent to, circle II. The area of circle I is $4$ sq. cm. Then the area of circle II, in sq. cm, is

• A. $8$
• B. $\sqrt{2}$
• C. $8\sqrt{\pi }$
• D. $16$
• E. $16\sqrt{2}$

Answer 1

Answer: (D)

$16$

Given : $m+n=10$ , $\sqrt{mn}=t$

$\Rightarrow t=\sqrt{m(10-m)}$

$m$ and $t$ are integers.

Also $m(10-m)\ge 0$

or $m(m-10)\le 0$

$\to m\in [0,10]$

$\Rightarrow m=0,1,2,......10$

But $t$ is also integer.

Hence possible values of $m$ are

$m=9$ and $m=2$

For which $t=3$ and $t=4$ respectively.

$\therefore t=3$ and $t=4$ is possible.

$\therefore C)$ Answer.