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Some interesting properties of the regular decagon

Ever thought of constructing a 4 units long segment, given the unit length? Here is another method: Construct a regular 10-gon with unit sides, and draw some diagonals and lengthen a side of it as shown in the figure. Then, by joining some intersection points being created, some 4 units long segments will also appear. This theorem has been automatically obtained by the software tool RegularNGons.