The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Given:

The radii of two circles are 19 cm and 9 cm respectively. 

To do:

We have to find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Solution:

Let the radius of the circle be $r$.

We know that,

Circumference of a circle of radius $r=2 \pi r$

Area of a circle of radius $r=\pi r^2$

Therefore,

The circumference of the circle of radius $19\ cm=2 \pi (19)$

$=38\pi$

The circumference of the circle of radius $9\ cm=2 \pi (9)$

$=18\pi$

According to the question,

$2\pi r=38\pi+18\pi$

$2\pi r=56\pi$

$r=28$

Area of the circle $=\frac{22}{7} \times (28)^2\ cm^2$

$=22\times 112\ cm^2$

$=2464\ cm^2$

The radius and area of the circle are $28\ cm$ and $2464\ cm^2$ respectively.