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1 sat \ 0 replies \ @south_korea_ln OP 16 Jan \ on: [Not-so-daily puzzle] A fun geometry puzzle science
The answer is 171.21.
Actual numbers are in the notes.
Main steps:
  • Realize that one can draw a vertical line from the top to the tangent point, due to it being a quarter circle.
  • Set the origin at the tangent point
  • Use point (5,1) = G being part of the circle to obtain the radius of the circle R by using
  • With R = 13, we can use Pythagoras to find that the length of AB = 12.
  • We can find the angle t using the 5-12-13 triangle denoted by ABC corners.
  • Use the to find that , hence .
  • Apply Pythagoras on triangle ADE to find that and thus .
  • Use the ratios between sides of similar triangles ABC and FHG to find that the length of FG equals .
  • You have all the information to find the area of the big rectangle (136) and the remaining triangle forming the rest of the shaded region ().
  • Add up the two values to find the final answer.
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