RU-ALLRUSSIAN 1964 Problem 5

The convex hexagon ABCDEF has all angles equal. Prove that $\mathrm{AB - DE = EF - BC = CD - }$ FA.

(b) Given six lengths $a_{1}$ , ..., $a_{6}$ satisfying $a_{1} - a_{4} = a_{5} - a_{2} = a_{3} - a_{6}$ , show that you can construct a hexagon with sides $a_{1}$ , ..., $a_{6}$ and equal angles.