From Gogeometry :
Using :
- BGC is congruent to BEA (by rotation of PI/2)
- BA⊥BC, BE⊥BG => AE⊥CG
- Define H such as AHD is the translation of BGC
- AHD is congruent to BGC (by translation)
- => BG=AH=EF and BG//AH//EF
- AE⊥CG, DH//CG => AE⊥DH
- EF=AH and EF//AH => AE=HF and AE//HF
- HF//AE and AE⊥DH => HF⊥DH
- Therefore x^2=2 a^2 or x=2√a