Given segments $a, b$ and $c$. Using

a compass and a straightedge, construct a segment $x$, such that $x: a=b: c$.

#
Use the theorem of proportional segments.

## Solution

On one side of an angle (not equal to $180^{\circ}$) with vertex $O$, sequentially lay off segments $O C=c$ and $C B=b$ (C between $O$ and $B$), and on the other side, lay off segment $O A=a$. Draw a line through point $B$ parallel to $A C$. Let this line intersect line $O A$ at point $D$. By the theorem of proportional segments, $A D: O A=B C: O C$, or $A D: a=b: c$, that is, $O D$ is the desired segment $x$.