A coffee break geometry problem #4

Geometry Level 4

The radius of the smallest circle is equal to

\((\lim_{x \to 1} \frac{3x^2-5x+2}{x^2-1})\)\((\lim_{x \to 5} \frac{20x-100}{x^2-25})\)

The circles with a medium size each have a radius 2 times that of the smallest circle. The largest circles each have a radius 4 times that of the smallest circle.

BG is perpendicular to ED. The line segment AC bisects \(\triangle\)ABD into equal parts.

Find the area of the shaded regions.

Extra information:

  • BC = CD = EF = GF
  • EA = AD
  • BA = AG
  • ED = BG
  • Point 'A' is the center of the smallest circle.
  • All line segments between the points are straight lines.

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