Star, Six Pentagons and Golden Ratio

The following has been posted by Tran Quang Hung at the CutTheKnotMath facebook page.

Reflect a regular pentagon $ABCDE\,$ in each of its sides. Join the vertices of the so obtained pentagons skipping two at a time.

Star, Six Pentagons and Golden Ratio

The resulting star cuts the sides of the pentagon $ABCDE\,$ in the Golden Ratio.

The diagram hides additional secrets that can be gleaned from the applet below:

Created with GeoGebra

In particular, there are additional occurences of the Golden Ratio. To discover them, you'll need to two or three boxes checked up.

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