Can YOU find the length with only one measure?

Geometry Level 1

Consider the above diagram, with:

  • \(AE=AD\)
  • Square \(BCDE\), with a circle circumscribed.
  • \(CD=2\sqrt{2}\)
  • \(\frac{BE}{AE}\) can be written as \(\frac{\sqrt{a}}{\sqrt{b+(c-\sqrt{d}) ^ k}}\), where every variable is equal to a natural number under 10.
  • \(y=k ^ a-(d ^ b)^c)\)
  • \(\frac{y}{a}\) can be written as \(\frac{f}{g}\), where \(gcf(g, f)=1\)
  • \(f-g=x\)

What is the value of \(x\)?


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