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:
Answer & explanation
Correct answer: option 1
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°