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