Question

Two circles touch externally. The sum of their areas is 130 $\pi$ sq cm and the distance between their centres is 14 cm The radii of the circles are

• A. $11,3$
• B. $12,4$
• C. $5,8$
• D. $4,6$

Answer 1

The correct option is A $11,3$

Let the radii of the two circle be $r_{1}and{r}_2$ respectively

They touch externally $r_1+r_2=14$

According to the question

$\pi r_1^2+\pi r_2^2=130\pi$

$\Rightarrow r_1^2+r_2^2=130$

Now ${(r_1+r_2)}^2=r_1^2+r_2^2+2r_1{r}_2$

${14}^2=130+2r_1{r}_2\left[By\left(i\right)and\left(ii\right)\right]$

$\Rightarrow 2r_2{r}_2=196-130=66$

$\Rightarrow r_1{r}_2=33$

$\therefore {(r_1-r_2)}^2=r_1^2+r_2^2-2r_1{r}_2$

$=130-66=64$

$\Rightarrow r_1-r_2=\sqrt{64}=8$

Solving equations (i) and (iv) we have

$r_1=11cm$ and $r_2=3cm$