Prove that, given any three parallel lines, an equilateral
triangle always exists with one vertex on each of the three lines.
*(In the problem 'Pareq Calc' the existence of the equilateral
triangle was assumed.)*

If you have Java enabled, it may help to use the dynamic diagram
below which shows three parallel lines and the fixed point
**A** on one of the lines. The points
**B** and **C** are free to move along
the other two parallel lines in such a way that the lengths
**AB** and **AC** are always equal.

*Click and drag the red points.*