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In a cyclic quadrilateral
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In a cyclic quadrilateral
A
B
C
D
ABCD
A
B
C
D
, chord
A
D
AD
A
D
subtends
∠
A
B
D
\angle ABD
∠
A
B
D
and
∠
A
C
D
\angle ACD
∠
A
C
D
. (a) Prove that
∠
A
B
D
=
∠
A
C
D
\angle ABD = \angle ACD
∠
A
B
D
=
∠
A
C
D
. (b) If
∠
A
B
D
=
(
4
x
−
6
)
∘
\angle ABD = (4x - 6)^{\circ}
∠
A
B
D
=
(
4
x
−
6
)
∘
and
∠
A
C
D
=
(
2
x
+
30
)
∘
\angle ACD = (2x + 30)^{\circ}
∠
A
C
D
=
(
2
x
+
30
)
∘
, find
x
x
x
.
Related theory
Circles
Circle angle properties
Angle subtended by a chord
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