There is a point $P$ and a circle. Draw a secant from $P$ $(P A B$ or $A P B)$ such that the chord $A B$ has a given length, $k$.
Given a circle with center $O$, we draw a tangent circle from any position of a chord $CD$ of length $k$. Drawing tangents from $P$ to this circle, we obtain points $A$ and $B$ on the given circle.

Let the radius of the given circle be $R$, and the radius of the tangent circle be $r$, then

$$
AB = 2 \sqrt{R^2 - r^2} = CD = k
$$

(Tibor Pálos, Budapest.)