Gogeometry Problem 1

From Gogeometry




Using :


  • Let b=AD=DC and d=BC
  • ∠BAC= ∠CBD and ∠BCD= ∠BCA
  • => ΔCAB is similar to ΔCBD
  • =>AC/BC=CB/CD=AB/BD => 2b^2=d^2, which means that d is the hypothenuse of a right triangle with side b
  • Define C’ such as ΔDBC’ is the symmetry of ΔDBC by BD
  • => ΔDBC’ is congruent to ΔDBC
  • ∠BDC=180°-45°=135° = ∠BDC’ => ∠CDC’=360-135-135=90°
  • => CC’=d and ΔCBC’ is equilateral
  • ∠DBC= ∠DBC’= 2x=60°
  • Therefore x=30°

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