Gogeometry Problem 256

From Gogeometry



SolutionUsing :

Additional points
Inscribed angles in a circle
congruent triangles
Equilateral triangle

  • CAD intercepts arc CD such as CBD => ∠CAD= ∠CBD
  • Define D’ n AD such as AD’C is congruent to BDC
  • => AD’=f and ∠ACD’= ∠BCD
  • ∠ACD= ∠ACB+ ∠BCD=Π/3+ ∠BCD
  • And ∠ACD= ∠ACD’+ ∠D’CD=∠BCD+ ∠D’CD => ∠D’CD = Π/3
  • CDA intercepts arc CA such as ABC => ∠CDA= ∠ABC=Π/3
  • ∠D’CD = Π/3 and ∠CDA= ∠CDD’= Π/3 => ΔD’CD is equilateral
  • =>D’D=CD=e
  • d=AD=AD’+D’D therefore d=e+f



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