Find the area of the square in that figure.

areacirclesgeometrytrigonometry

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For the above figure,

  • Figure is symmetric with respect to both $AC$ & $BD$
  • $ADC,ABC,DFBE$ are circle or part of circle
  • The outer quadrilateral is a square
  • Extended upper sides touch extended arch of $ADC$
  • Extended lower sides touch extended arch of $ABC$
  • $AC=6$ $\mathrm{cm}$, $BD=2$ $\mathrm{cm}$

Find green, black and white colored areas.

I have found the green and the black area using area of circle & trigonometry. Could you please tell me how can I find the side length of the square so that I can find the area of that square?

Best Answer

HINT.

The line connecting the center of circle $ADC$ with a tangency point must form an angle of $45°$ with line $BD$.

enter image description here

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