Golden Ratio in an Irregular Pentagon, Construction I

The following construction has be devised by Bui Quang Tuan:

 

Let X, Y, Z be collinear, Y between X and Z, such that XY/YZ = φ, the golden ratio. Construct

  • A reflection of Y in X,
  • Choose any point D not on the line XYZ,
  • C reflection of D in Z,
  • C' the intersection of CY and AD,
  • D' the intersection of DY and AC,
  • B reflection of D in midpoint of YD',
  • E = reflection of C in midpoint of YC'.
 

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Some properties of so constructed pentagon ABCDE are discussed elsewhere. There is an additional construction of pentagons of this kind.

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