In the following figure (not to scale), at the centre O if the chord AB subtends double the angle that is subtended by chord CD and the angle ∠AEB = 2∠AOB, then ∠COD is equal to:

30°

We know that,

Chord AB subtends double the angle that is subtended by chord CD. 

∠AEB = 2 ∠AOB,

∠AOB = 2 ∠COD

∠OBE = ∠OAE = 90°

In AOBE

∠AOB + ∠AEB + ∠OBE + ∠OAE = 360°

= ∠AOB + ∠AEB + 90° + 90° = 360°

= ∠AOB + 2 ∠AOB = 360° - 180°

= 3 ∠AOB = 180°

= ∠AOB = 180°/3

= ∠AOB = 60°

= 2 ∠COD = 60°

= ∠COD = 30°