Constructing the midpoint of a line segment
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In this exercise you are given two points \(X\) and \(Y\). Your task is to construct a point \(Z\) such that \(|XZ| = |YZ|\). The point \(Z\) is then the midpoint of the segment \(XY\).
There are a number of ways to do this construction. One method (used by Euclid) is to use the angle bisector tool from the previous construction.
The diagram contains an example of two points \(A\) and \(B\) and a point \(M\) which is the midpoint of \(AB\).
Hint. This exercise is explained in Euclid Book I, Proposition 10.
