Bisecting an angle

In this exercise you are given three points \(X\), \(Y\) and \(Z\). Your task is to construct a point \(W\) such that \(\angle XYW = \angle WYZ\). Equivalently, the goal is to construct a ray from \(Y\) which bisects the angle \(\angle XYZ\).

The diagram contains an example of three points \(A\), \(B\) and \(C\) and a point \(D\) such that \(\angle ABD = \angle DBC\).

Hint. This exercise is explained in Euclid Book I, Proposition 9.