Question

Two circles touch each other externally.If the sum of their areas is $130\pi c{m}^2$ and the distance between their centres is $14cm$. Find the sum of their radii.

• A. 11 cm
• B. 19 cm
• C. 14 cm
• D. 17 cm

Answer 1

The correct option is C

14 cm

According to the question,

$x+y=14$ ….(1)

$\pi x^2+\pi y^2=130\pi$

$\Rightarrow x^2+y^2=130$…..(2)

From equation (1), we get $y=14–x$

Put $y=14–x$ in equation (2), we get

$\Rightarrow x^2+(14-x{)}^2=130$

On solving, we get

$x=11,3$

If $x=11,y=14-11=3$

If $x=3,y=14-3=11$

So radius of each circle = $11cm,3cm$

Hence, sum of their radii = $14cm$