Constructing a circle centred on a line and passing through two given points

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In this exercise you are given two points \(X\), \(Y\) and a line \(PQ\). Your task is to construct a circle which passes through the two points \(X\), \(Y\) and has centre on the line \(PQ\).

In the diagram below you can see an example. The two points \(B\), \(C\) and the line \(DE\) are given. The orange circle has centre \(O\) on the line \(DE\) and passes through both points \(B\), \(C\).


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