This is another tough nut mind bender, and we have to give a proof of existence. The conjecture is that, given any set of three parallel lines, there always exists an equilateral triangle with one of its vertices on each of the lines. The trouble with this sort of mathematics is that there are infinitely many possible cases. It means nothing that the conjecture holds true in every case we test because it might still break down in a case we have not tried. So what can be done? Playing with the dynamic diagram suggests that the length of BC changes - how does it change?