Question

In the figure O is the centre of the circle, A=40 Find AOB​

Answer 1

Answer:

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Answer 2

Answer:

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference

So we get

∠AOB=2∠ACB

From the figure we know that

∠ACB=∠DCB

It can be written as

∠AOB=2∠DCB

We know that

∠DCB=

2

1

∠AOB

By substituting the values

∠DCB=

2

40

o

By division

∠DCB=20

o

In △DBC

Using the angle sum property

∠BDC+∠DCB+∠DBC=180

o

By substituting the values we get

100

o

+20

o

+∠DBC=180

o

On further calculation

∠DBC=180

o

−100

o

−20

o

By subtraction

∠DBC=180

o

−120

o

So we get

∠DBC=60

o

From the figure we know that

∠OBC=∠DBC=60

o

So we get

∠OBC=60

o

Therefore , ∠OBC=60

o

.