IN THE CIRCLE WITH CENTRE O . AB=BC=CD AND ANGLE AOB =40 FIND ANGLE OBD
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Step-by-step explanation:
"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
.
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