From a given point, we draw a tangent and a secant to a given circle. The length of the tangent is $18 \mathrm{~cm}$, and the part of the secant inside the circle is $27 \mathrm{~cm}$. What is the length of the other part of the secant?
Let the part of the secant outside the circle be $x$, then

$$
x(x+27)=18^{2}
$$

or

$$
x^{2}+27 x-324=0
$$

from which the positive root $x=9$, so the part of the secant outside the circle is $9 \mathrm{~cm}$.

(Miksa Lusztig, Pécs.)

Number of solutions: 22.