Question

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

Answer 1

Answer:

join CO &DO

angle BCD= angle ABC =25°[alt.int.angle]

angle BOD=2angle BCD =50° [therefore arc BD makes angle BOD at the centre and angle BCD at point on the circle]

Answer 2

∠CED = 40° Chord CD is parallel to diameter AB & Angle ABC = 25

Step-by-step explanation:

CD ║ AB

=> ∠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.

=> ∠BOD = 2∠BCD

=> ∠BOD = 2 × 25° = 50°

Similarly, ∠AOC = 2∠ABC

=>  ∠AOC = 2 × 25° = 50°

AB is a Diameter hence passing through the centre.

=> ∠AOC + ∠COD + ∠BOD = 180°

=>  50° + ∠COD + 50° = 180°

=>∠COD  = 80°

∠CED=∠COD /2

=> ∠CED= 80°/2 = 40°

=>∠CED = 40°

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