Question

4. In the fig. O is the centre of the circle. find angle AOB
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Answer 1

Answer:

100°

Step-by-step explanation:

Join OC

OA= OC (Radii of Circle)

∠OAC=∠OCA= 20° (Angle opposite to equal sides are equal to each other)

Similarly,

OC=OB (Radii of Circle)

∠OBC=∠OCB= 30° (Angle opposite to equal sides are equal to each other)

∠ACB=∠OCA+∠OCB

∠ACB= 20°+30°

∠ACB= 50°

2∠ACB= ∠AOB (Theorem 10.8)

2(50)= ∠AOB

100°= ∠AOB

NOTE:- Theorem 10.8 states that 'The angle subtended by the arc at the center is double the angle subtended by it at any point on the remaining part of the circle.'

Hope It Helps :)