Question

Find the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius $19$ cm and $9$ cm.

Answer 1

Let $r$ be the radius of the new circle.

Now sum of circumference of the circles having radius $19$ cm and $9$ cm is $=2\pi \times (19+9)=2\pi \times 28$ cm.

Then according to the problem,

$2\pi \times r=2\pi \times 28$

or, $r=28$.

So the radius of the new circle is $28$ cm.