The sum of the area of a circle and an equilateral triangle inscribed in the circle is $50 \mathrm{~cm}^{2}$. Calculate the area of the triangle and the circle.
In the context of the task

$$
r^{2} \pi+\frac{3 r^{2}}{4} \sqrt{3}=50
$$

from which

$$
r^{2}=\frac{200}{3 \sqrt{3}+4 \pi}
$$

The area of the circle is $35.37 \mathrm{~cm}^{2}$, and that of the triangle is $14.63 \mathrm{~cm}^{2}$.

(József Martini, Pozsony.)

The problem was also solved by: Dévai E., Erdős V., Fekete M., Friedländer H., Füstös P., Havas E., Heimlich P., Horti V., Jánosy Gy., Kepes I., Kiss J., Lázár B., Meleghy Gy., Paunz A., Pichler S., Schuster Gy., Tandlich E., Tóth B., Vetter E., Wáhl V., Wottitz R.