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.