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 circumference of the two circles.

Let r be the radius of the circle whose circumference is equal to the sum of the circumference of two circles of radii 19 cm and 9 cm.

\(\therefore \) \( 2 \pi r \ = \ 2 \pi (19) \ + \ 2 \pi (9) \)

\( \Rightarrow \ r \ = \ 19 \ + \ 9 \ = \ 28 \)

Hence, the radius of the new circle is 28 cm.