The circumferences of two circles are in the ratio $2:3$. Find the ratio of their areas.

Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii $15 \text{cm}$ and $18 \text{cm}$.

The radii of two circles are $8 \mathrm{cm}$ and $6 \mathrm{cm}$, respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

The radii of two circles are $19 \mathrm{cm}$ and $9 \mathrm{cm}$, respectively. Find the radius and area of the circles which has it circumference equal to the sum of the circumferences of the two circles.

The area of a circle inscribed in an equilateral triangle is $154 {\mathrm{cm}}^2$. Find the perimeter of the triangle.