Question

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.

Answer 1

Let the radius of the third circle be R.
Circumference of the circle with radius $R=2\pi R$
Circumference of the circle with radius $19cm=2\pi \times 19=38\pi cm$
Circumference of the circle with radius $9cm=2\pi \times 9=18\pi cm$
Sum of the circumference of two circles $=38\pi +18\pi =56\pi cm$
Circumference of the third circle $=2\pi R=56\pi$
$\Rightarrow 2\pi R=56\pi cm$
$\Rightarrow R=28cm$
The radius of the circle which has circumference equal to the sum of the circumferences of the two circles is 28 cm.