Most Beautiful Math Olympiad Problem

Most Beautiful Problem In Mathematical Olympiad 

This beautiful problem from INMO 1993

Although this problem can be solved using vector math, the following solution using pre high school math is in my view one of the most elegant solutions I have come across:

1.Draw an equilateral triangle with side length 9.

2.Chop off equilateral triangles at each corner of side length 1, 2 and 3.

3.The resulting hexagon satisfies the properties