Question

In the adjoining figure ,O is the centre of the circle.Chord CD is parallel to the diameter AB.If angle ABC is 15 °, calculate angle CED​

Answer 1

Step-by-step explanation:

Given ∠ABC=15°

o

Now, ∠AOC subtended by the chord AC at the centre O of circle will be double the ∠ABC subtended by same chord AC at point B on corresponding segment of circle thus

∠AOC=2∠ABC=2×15°=30°

∠BOD=∠AOC=30°

But

∠AOC+∠COD+∠BOD=180°

30°+∠COD+30°=180°

∠COD= (180-60)°= 120°

Now, ∠COD subtended by the chord CD at the centre O of circle will be double the ∠CED subtended by same chord CD at point E on corresponding segment of circle thus

∠COD=2∠CED

120° =2∠CED

∠CED= 120°/2= 60°

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