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Byju's Answer
Standard IX
Mathematics
Theorem on Cyclic Quadrilateral and Its Converse
In the given ...
Question
In the given figure,
O
is the centre of circle and
∠
D
A
B
=
50
o
. Calculate the values of
x
and
y
.
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Solution
It is given that
O
is the centre of the circle and
∠
D
A
B
=
50
o
We know that the radii of the circle are equal
O
A
=
O
B
From the figure we know that
∠
O
A
B
+
∠
O
B
A
+
∠
A
O
B
=
180
o
By substituting the values
50
o
+
50
o
+
∠
A
O
B
=
180
o
On further calculation
∠
A
O
B
=
180
o
−
50
o
−
50
o
By subtraction
∠
A
O
B
=
180
o
−
100
o
So we get
∠
A
O
B
=
80
o
From the figure we know that
A
O
D
is a straight line
It can be written as
x
=
180
o
−
∠
A
O
B
By substituting the values
x
=
180
o
−
80
o
By subtraction
x
=
100
o
We know that the opposite angles of a cyclic quadrilateral are supplementary
So we get
∠
D
A
B
+
∠
B
C
D
=
180
o
By substituting the values
50
o
+
∠
B
C
D
=
180
o
On further calculation
∠
B
C
D
=
180
o
−
50
o
By subtraction
y
=
∠
B
C
D
=
130
o
Therefore the value of
x
is
100
o
and
y
is
130
o
.
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Q.
In the given figure, O is the centre of the circle and
∠DAB = 50°. Calculate the values of x and y.