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:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 30o
| Understanding | Application |
| Angle made on a tangent is perpendicular to the radius. |
Given that, ⇒ ∠AEB = 2 ∠AOB & ⇒ ∠AOB = 2 ∠COD We can infer that ⇒ ∠OBE = ∠OAE = 90°(By the given property) In quadrilateral AOBE ⇒ ∠AOB + ∠AEB + ∠OBE + ∠OAE = 360° ⇒ ∠AOB + ∠AEB + 90° + 90° = 360° ⇒ ∠AOB + 2 × ∠AOB = 180° ⇒ ∠AOB = 60° ⇒ 2 ∠COD = 60° ⇒ ∠COD = 30° |