If the side of the hexagon and that of the decagon inscribed in the same circle be added together, the whole straight line has been cut in extreme and mean ratio, and its greater segment is the side of the hexagon.
Proof
The hexagon side equals the radius (IV.15); the decagon side
satisfies the 36-72-72 triangle relations (IV.10); their sum is in
the golden ratio to the hexagon side.