The figure shows a regular hexagon ABDEF inscribed in a circle. If point G is on arc BC, GA = a, GB = b, GC = c,
GD = d, GE = e, GF = f, prove that a + b + c d = e + f.

Geometry software that can be used to learn and research:

Geometry Expressions, Cabri, Cinderella, GeoGebra, Geometer Sketchpad, C.a.R., TracenPoche, Mathematica.