Question

Two circles touch each other externally. The sum of their areas is $490\pi$ $c{m}^2$. Their centres are separated by 28 cm. Find the difference of their radii (in cm).

Answer 1

Let the radii of the circles be denoted by $r_1$ cm and $r_2$ cm where $r_1\ge r_2$. As the circles touch each other externally, distance between their centres = sum of their radii.

$r_1+r_2=28$ ....(1)

Also, $\pi (r_1{)}^2+\pi (r_2{)}^2=490\pi$

$(r_1{)}^2+(r_2{)}^2=490$ .........(2)

Squaring both sides of equation 1, we get,

$(r_1{)}^2+(r_2{)}^2+2\left(r_1\right)\left(r_2\right)=784$

$r_1.r_2=147$ ...(3)

Solving equation 1 and 3, we get,

$r_1=21$ and $r_2=7$ $(r_1\ge r_2)$

Therefore, required difference = 14 cm.