A hint for Q2 on Homework 2

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The diagram below shows the configuration of lines from Question 2 on Homework 2. The hint is as follows: first apply Desargues' theorem to the triangles \(\Delta QRS\) and \(\Delta UVP\). These two triangles are in perspective from the point \(B\), therefore they are in perspective from a line. Since \(C = QS \cap UP\) and \(A = RS \cap PV\) then this line must be \(AC\). Therefore we know that \(QR \cap UV\) lies on the line \(AC\).

To finish the problem, use the a similar idea on the pair of triangles \(\Delta PQR\) and \(\Delta TUV\).