8.5. Given a point $A$ and a circle $S$. Draw a line through point $A$ such that the chord cut off by the circle $S$ on this line has a given length $d$.
8.5. Let $R$ be the radius of the circle $S$, and $O$ its center. If the circle $S$ intersects a line passing through point $A$ at chord $P Q$ and $M$ is the midpoint of $P Q$, then $O M^{2}=O Q^{2}-M Q^{2}=R^{2}-d^{2} / 4$. Therefore, the desired line is tangent to the circle of radius $\sqrt{R^{2}-d^{2} / 4}$ centered at $O$.