Draw circle centred at A and any chord CD

   AC = AD                (radius of circle)

   ∇ACD is isosceles      (2 sides equal)

∴  ∠ACD = ∠ADC = α

∴  ∠CAD = 180 - 2α

Draw any chord CE

   ∠CED = 180 - (∠ECD + ∠EDC)

Draw radius AE

     AE = AD            (radius of circle) 

   ∇AED is isosceles    (2 sides equal)

∴  ∠AED = ∠ADE = γ

     AC = AE            (radius of circle) 

   ∇ACE is isosceles    (2 sides equal)

∴  ∠AEC = ∠ACE = δ

   ∠CED = 180 - ∠ECD - ∠EDC  (see above)

    γ-δ = 180 - (α-δ) - (γ+α)

        = 180 - 2α - (γ-δ)

 2(γ-δ) = 2(90-α)

∴   γ-δ = 90-α

   ∠CED = 90-α

but

   ∠CAD = 180 - 2α            (proved above)

∴  ∠CED = ∠CAD/2