Transferring a length from one point to another

Now you can use the Equilateral Triangle Construction to transfer a length from one point to another. Given a line segment

$XY$ and a point

$Z$ , can you construct a point

$W$ such that

$|XY| = |WZ|$ ? Equivalently, can you draw a circle centred at

$Z$ with radius

$|XY|$ ?

As an example, the diagram below contains a line segment

$AB$ and a circle centred at

$C$ with radius

$AB$ . Any point

$D$ on this circle will automatically satisfy

$|AB| = |CD|$ .

Just as for the previous exercise, the tools you can use are limited, since all you have is a ruler and compass as well as your knowledge of how to construct an equilateral triangle.

Hint. This exercise is explained in Euclid Book I, Proposition 2.