Constructing the golden ratio

In this exercise you are given a line segment \(AB\) with \(|AB|=1\). Your task is to construct another point \(D\) on the line \(AB\) such that \(|BD|\) is equal to the golden ratio \(\frac{1}{2}(1 + \sqrt{5})\). In the same way as some of the earlier exercises, you can use the length tool to check your answer.

As an example, the diagram contains a point \(C\) on the line \(AB\) such that \(|AC| = \frac{1}{2}(1 + \sqrt{5})\). The rectangle with one sidelength equal to the golden ratio and the other sidelength equal to one is often used in architecture and art and design.