Construction a Golden Rectangle

[Acorn]

OK, perhaps the concept is a bit too exotic but keep it in mind for future reference.

Here is a construction that delivers a Golden Rectangle from an initial pentagon.

1. Create a Red pentagon, with rotation 180°.
2. Clone it, colour it Green and change to a circle.
3. Place its centre on the pentagon left base corner.
4. Shift-drag until the circle's edge touches the pentagon's opposite sides. [I used a mixture of Guides and Zooms as there is no snap point unless you add set the circle's rotation as 36° (or rotate all the construction by the same)!]
5. Clone the pentagon, colour it Blue and change to a square.
6. Resize and position its base to match the pentagon.
7. Drag up the top to touch the green circle.

I have left a simpler approach outstanding should anyone still want to have a go.

Acorn