Interactive picture for Q4 on Homework 1

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You can click and drag the points \(A\), \(B\) and \(C\) to move the vertices of the triangle. Moving the point \(P\) will move the line \(AP\), and moving the point \(Q\) (which is restricted to lie on \(AP\)) will move the line \(CQ\). This determines all of the other points in the picture.

The goal of the question is to use Ceva's theorem to show that the lines \(AX_2\), \(BY_3\) and \(CZ_1\) are concurrent. (In the next homework we will prove this using Desargues' theorem.)