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Question

In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If ABC=25, calculate CED.


Solution


∠BCD = ∠ABC = 25° (Alternate angles)
Join CO and DO.
We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by an arc at any point on the circumference.
Thus, ∠BOD = 2∠BCD
⇒∠BOD = 2 × 25° = 50°
Similarly, ∠AOC = 2∠ABC
 ∠AOC = 2 × 25° = 50°
AB is a straight line passing through the centre.
i.e., ∠AOC + ∠COD + ∠BOD = 180°
⇒ 50° + ∠COD + 50° = 180°
⇒ ∠COD = (180° – 100°) = 80°
⇒∠CED=12​​​​​​​∠COD
⇒∠CED=(12×80°)=40°
∴ ∠CED = 40°

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